polyradical with very high spin of s ) 10 and its derivatives: s

Organic Spin Clusters. A Dendritic-MacrocyclicPoly(arylmethyl) Polyradical with Very High Spin of S ) 10

and Its Derivatives: Synthesis, Magnetic Studies, andSmall-Angle Neutron Scattering

Suchada Rajca,*,† Andrzej Rajca,*,† Jirawat Wongsriratanakul,† Paul Butler,‡ andSung-min Choi§

Contribution from the Department of Chemistry, UniVersity of Nebraska,Lincoln, Nebraska 68588-0304, and The National Center for Neutron Research, NIST,

Gaithersburg, Maryland 20899-8562

Received December 5, 2003; E-mail: [email protected]; [email protected]

Abstract: Synthesis and characterization of organic spin clusters, high-spin poly(arylmethyl) polyradicalswith 24 and 8 triarylmethyls, are described. Polyether precursors to the polyradicals are prepared via modular,multistep syntheses, culminating in Negishi cross-couplings between four monofunctional branch (dendritic)modules and the tetrafunctional calix[4]arene-based macrocyclic core. The corresponding carbopolyanionsare prepared and oxidized to polyradicals in tetrahydrofuran-d8. The measured values of S, from numericalfits of magnetization vs magnetic field data to Brillouin functions at low temperatures (T ) 1.8-5 K), areS ) 10 and S ) 3.6-3.8 for polyradicals with 24 and 8 triarylmethyls, respectively. Magnetizations atsaturation (Msat) indicate that 60-80% of unpaired electrons are present at T ) 1.8-5 K. Low-resolutionshape reconstructions from the small-angle neutron scattering (SANS) data indicate that both the polyradicalwith 24 triarylmethyls and its derivatives have dumbbell-like shapes with overall dimensions 2 × 3 × 4 nm,in agreement with the molecular shapes of the lowest energy conformations obtained from Monte Carloconformational searches. On the basis of these shapes, the size of the magnetic anisotropy barrier in thepolyradical, originating in magnetic shape anisotropy, is estimated to be in the milliKelvin range, consistentwith the observed paramagnetic behavior at T g 1.8 K. For macromolecular polyradicals, with the elongatedshape and the spin density similar to the polyradical with 24 triarylmethyls, it is predicted that the valuesof S on the order of 1000 or higher may be required for “single-molecule-magnet” behavior, i.e.,superparamagnetic blocking (via coherent rotation of magnetization) at the readily accessible temperaturesT > 2 K.

Introduction

Molecules with large values of quantum spin numberS inthe electronic ground states may be viewed as models for or-ganic polymers with magnetic ordering.1-4 Design and synthesisof such molecules (polyradicals) must ensure that strongthrough-bond exchange interactions between multiple sites withunpaired electrons (radicals) are maintained.4 Even if very effi-cient synthetic methods for generation of radicals are employed,the finite probability that generation of radicals will not becomplete must be taken into account, i.e., formation of chemical

defects. Therefore, connectivity between radicals should be suchthat strong exchange interaction between the radicals is sustainedin the presence of small density of chemical defects.5-7

Furthermore, out-of-plane twistings of the conjugated systemmay lead to the ferromagnetic-to-antiferromagnetic couplingreversals, diminishing the net value ofS.8-12 The effectivenessof various approaches to this problem may be measured by thevalues ofS in the electronic ground state.4,13-19

† University of Nebraska.‡ National Center for Neutron Research. Present address: Neutron

Scattering Section, ORNL, Bldg 7962, 1 Bethel Valley Rd., P.O. Box 2008,Oak Ridge, TN 37831-6393.

§ National Center for Neutron Research. Present address: Departmentof Nuclear and Quantum Engineering, Korea Advanced Institute of Scienceand Technology, 373-1 Gusong-dong, Yusong-gu, Daejon 305-701,Republic of Korea.(1) Rajca, A.; Wongsriratanakul, J.; Rajca, S.Science2001, 294, 1503-1505.(2) Rajca, A.; Rajca, S.; Wongsriratanakul, J.J. Am. Chem. Soc.1999, 121,

6308-6309.(3) Rajca, A. Encyclopedia of Polymer Science and Technology, 3rd ed.;

Kroschwitz, J. I., Ed.; Wiley: New York, 2002.(4) Rajca, A.Chem.sEur. J. 2002, 8, 4834-4841.

(5) Rajca, A.; Utamapanya, S.J. Am. Chem. Soc.1993, 115, 10688-10694.(6) Rajca, A.; Rajca, A.; Padmakumar, R.Angew. Chem., Int. Ed. Engl.1994,

33, 2091-2093.(7) Rajca, A.; Rajca, S.; Desai, S. R.J. Am. Chem. Soc.1995, 117, 806-816.(8) Dvolaitzky, M.; Chiarelli, R.; Rassat, A.Angew. Chem., Int. Ed. Engl.1992,

31, 180-181.(9) Fang, S.; Lee, M.-S.; Hrovat, D. A.; Borden, W. A.J. Am. Chem. Soc.

1995, 117, 6727-6731.(10) Silverman, S. K.; Dougherty, D. A.J. Phys. Chem.1993, 97, 13273-

13283.(11) Kanno, F.; Inoue, K.; Koga, N.; Iwamura, H.J. Am. Chem. Soc.1993,

115, 847-850.(12) Rajca, A.; Rajca, S.J. Chem. Soc., Perkin Trans. 21998, 1077-1082.(13) Nakamura, N.; Inoue, K.; Iwamura, H.Angew. Chem., Int. Ed. Engl.1993,

32, 872.(14) Iwamura, H.; Koga, N.Acc. Chem. Res.1993, 26, 346-351.(15) Matsuda, K.; Nakamura, N.; Inoue, K.; Koga, N.; Iwamura, H.Bull. Chem.

Soc. Jpn.1996, 69, 1483-1494.

Published on Web 05/07/2004

6972 9 J. AM. CHEM. SOC. 2004 , 126, 6972-6986 10.1021/ja031548j CCC: $27.50 © 2004 American Chemical Society

Tetracosaradical (24-radical)1 and octaradical2 are designedas “organic spin clusters”.20-22 One of the key elements of thisdesign is theS ) 2 macrocyclic core, as illustrated bytetraradical3.7 Because ferromagnetic coupling through the 1,3-phenylene moiety is significantly stronger than that through the3,4′-biphenylene, “unpaired” electrons in the four branches andthe macrocyclic core can effectively be lumped into componentspins (S′).21,22 Such ferromagnetically coupledS′ ) 5/2, 5/2,5/2, 5/2, 4/2 spin pentamer should haveS ) 12 ground state;similarly, theS′ ) 1/2, 1/2, 1/2, 1/2, 4/2 spin pentamer shouldhaveS ) 4 ground state (Figure 1).22

Another aspect of molecules with large values ofS is themagnitude of their magnetic anisotropy barrier. Numeroustransition metal ion based molecules (clusters) show substantialbarriers for inversion of magnetization, thus acting effectivelyas “single-molecule-magnets” (SMM) at cryogenic tempera-tures.23,24The magnetic anisotropy of SMM’s is primarily basedon the single-ion anisotropies, especially of the Jahn-Teller

distorted ions.25 For organic polyradicals, in particular hydro-carbons, the contribution to magnetic anisotropy from the class-ical magnetic dipole-dipole interactions is expected to berelatively important.26 Therefore, it might be expected that thebarriers for coherent rotation of magnetization in organicpolyradicals may be related to the molecular shape of polyradicaland its spin density.4,26,27Such magnetic shape anisotropies maybe significant in polyradicals with elongated shapes.26,27

The title 24-radical1 with S) 10, which is the highest spinorganic molecule to date,4,22 provides an excellent model forstudy of both exchange coupling and the possibility of magneticshape anisotropy in organic macromolecules. This articledescribes details of synthesis and characterization of 24-radical1 and its homologue octaradical2 (Figure 1), including quan-titative magnetic studies. For1, shape determinations with small-angle neutron scattering (SANS) are reported. These studiesshould provide an insight into the magnetic behavior (e.g.,related to the magnetic shape anisotropy) in the first conjugatedpolymer with magnetic ordering.1,28

Results and Discussion

1. Synthesis of Polyethers.Modular and convergent synthesisis employed to prepare tetracosaether (24-ether)1-(OMe)24 andoctaether2-(OMe)8, precursors to 24-radical1 and octa-radical 2. The synthesis is carried out in two stages: (1)preparation of the tetrafunctionalized macrocyclic module7Ewith an effectiveC4V point group of symmetry (Scheme 1 andFigure 2); (2) attachment of four monofunctionalized dendritic821 or monoether920 modules to the macrocyclic module7E,using Negishi coupling (Scheme 2).29

Compound4 and diketone5 are prepared according to thepublished procedure.30 Bis(aryllithium), which is obtained viaLi/Br exchange on4, is condensed with the diketone5 to give

(16) Nishide, H.; Ozawa, T.; Miyasaka, M.; Tsuchida, E.J. Am. Chem. Soc.2001, 123, 5942-5946.

(17) Michinobu, T.; Inui, J.; Nishide, H.Org. Lett.2003, 5, 2165-2168.(18) Bushby, R. J.; McGill, D. R.; Ng, K. M.; Taylor, N.J. Chem. Soc., Perkin

Trans. 21997, 7, 1405-1414.(19) Anderson, K. K.; Dougherty, D. A.AdV. Mater. 1998, 10, 688-692.(20) Rajca, A.; Rajca, S.J. Am. Chem. Soc.1996, 118, 8121-8126.(21) Rajca, A.; Wongsriratanakul, J.; Rajca, S.J. Am. Chem. Soc.1997, 119,

11674-11686.(22) Rajca, A.; Wongsriratanakul, J.; Rajca, S.; Cerny, R.Angew. Chem., Int.

Ed. 1998, 37, 1229-1232.(23) Lis, T. Acta Crystallogr., Sect. B1980, 36, 2042-2046.(24) Sessoli, R.; Gatteschi, D.; Caneschi, A.; Novak, M. A.Nature1993, 365,

141-143.

(25) Boskovic, C.; Pink, M.; Huffman, J. C.; Hendrickson, D. N.; Christou, G.J. Am. Chem. Soc.2001, 123, 9914-9915.

(26) Rajca, A.Chem. ReV. 1994, 94, 871-893.(27) Aharoni, A. Introduction to the Theory of Ferromagnetism, 2nd ed.;

Oxford: Oxford, U.K., 2000.(28) (a) The alternative design of organic spin clusters, addressing the develop-

ment of net ferri- or ferromagnetic correlations in the conjugated polymerwith magnetic ordering, is described in the following: Rajca, A.; Wong-sriratanakul, J.; Rajca, S. Organic Spin Clusters: Macrocyclic-MacrocyclicPoly(arylmethyl) Polyradicals with Very High SpinS) 5-13.J. Am. Chem.Soc.2004, 126, in press. (b) The design annelated macrocyclic organicspin clusters, addressing the dimensionality of the conjugated polymer withmagnetic ordering, is described in the following: Rajca, A.; Wongsrira-tanakul, J.; Rajca, S.; Cerny, R. L. Organic Spin Clusters: AnnelatedMacrocyclic Polyarylmethyl Polyradicals and Polymer with Very High SpinS ) 6-18. Chem.sEur. J. 2004, 10, in press.

(29) (a) Negishi, E.; King, A. O.; Okukado, N.J. Org. Chem.1977, 42, 1821-1823. (b) Negishi, E.; Takahashi, T.; King, A. O.Org. Synth.1987, 66,67-74.

(30) Rajca, A.; Lu, K.; Rajca, S.J. Am. Chem. Soc.1997, 119, 10335-10345.

Figure 1. Target polyradicals1 and 2 as spin pentamers and tetra-radical3.

Scheme 1. Synthesis of Diols 6 and Tetraethers 7

Organic Spin Clusters A R T I C L E S

J. AM. CHEM. SOC. 9 VOL. 126, NO. 22, 2004 6973

macrocyclic diols as five cis/trans isomers6A-E in overall yieldof 34-46% (Scheme 1).

(6A-E are labeled alphabetically in the order of increasingpolarity on silica.) Although all five possible isomers areisolated, only6A (14-17%), 6D (5-10%), and6E (4%) arereadily separable on silica; the remaining two isomers areisolated as a mixture of6B and 6C (8-14%, 3.5:1-2.5:1),though small amounts of both isomers are obtained forspectroscopic characterization. Etherification of diols6A,D,Ewith MeI yields the corresponding ethers7A (62%), 7D(63-84%), and7E (38-61%); analogously, a mixture of diols6B,C (3.5:1) provides a mixture of ethers7D,C (88%, 3.6:1),i.e., diols6B,D are related to an identical ether7D.

All five possible cis/trans isomers of diols6 and all fourpossible cis/trans isomers of tetraethers7 are shown in Figure2. Their point groups of symmetry, as expected under conditionsof fast exchange between different calix[4]arene conformations,are also indicated. For each isomer, FAB MS gives the expected(M - OCH3)+ cluster ions; the diols6 show additional, intense

(M - OH)+ cluster ions. Measured and calculated isotopicdistributions for both cluster ions show satisfactory agreement.IR spectra show the presence of the OH groups in diols, as twobroad peaks (6A-D) or one broad peak (6E) in the 3400-3600 cm-1 range. The1H and 13C NMR spectra allow forunambiguous assignment of diols6A,B,D, and the correspond-ing tetraethers7A,D (Tables 1s-3s, Supporting Information).However, the most symmetric diols6C,E (and the correspondingtetraethers7C,E) have similar NMR spectral patterns, precludingtheir assignment by NMR spectroscopy (Tables 1s-3s, Sup-porting Information). These two isomer sets are assigned withthe help of X-ray crystallography.

The molecular structure from X-ray crystallography of7Eshows the all-cis isomer; i.e., all four methoxy groups are locatedon the same face of the macrocycle (Figure 3). This impliesthat isomer7C must have all-trans methoxy groups. Interest-ingly, the calix[4]arene macrocycle7E adopts the 1,3-alternateconformation.31,32One of thetert-butyl groups is disordered overtwo positions. The carbon atoms of thetert-butyl groups showlarge displacement parameters, especially C16A-C18A, whichare in the vicinity of the solvent void. This suggests theflexibility of the calix[4]arene macrocycle. The inefficientpacking of the calix[4]arene results in large voids that containan unknown amount of solvent (Experimental Section).

TheC4V-symmetric isomer7E, which shows 4-fold symmetryon the NMR scale at ambient temperature and is readilyseparable, is selected as the macrocyclic module. Conditionsfor the Li/Br exchange for the branch module8 are optimizedby isolation of monodeuterated module8-D after the MeODquench of the corresponding aryllithium (Scheme 2). Negishicouplings between the branch modules (8 and 9, 6 equiv asorganozinc derivatives) and the macrocyclic module (7E, 1equiv) give 24- and 8-ethers1-(OMe)24 and 2-(OMe)8 in13-40 and 12-16% isolated yields, respectively (Scheme 2).

The following side products are isolated: homocouplingproducts of the branch modules (10 and11, ∼10%); debromi-nated branch module (module8-H, 23%); tricoupling product(12-(OMe)19, 1%) (Chart 1).

(31) Gutsche, C. D.Calixarenes ReVisited; RSC, Cambridge, U.K., 1998; Chapter4.

(32) Rajca, A.; Padmakumar, R.; Smithhisler, D. J.; Desai, S. R.; Ross, C. R.;Stezowski, J. J.J. Org. Chem.1994, 59, 7701-7703.

Figure 2. Cis/trans isomers of calix[4]arene diols6 and tetraethers7. Open and closed circles correspond to the relative orientation of the OMe (blue) andOH (red) groups.

Scheme 2. Synthesis of Polyethers 1-(OMe)24 and 2-(OMe)8

A R T I C L E S Rajca et al.

6974 J. AM. CHEM. SOC. 9 VOL. 126, NO. 22, 2004

The target polyethers (and the isolated side products) showexpected monocharged (M- OCH3)+ cluster ions as the mostintense signals in the high-mass range of FAB MS (Figure 1s,Supporting Information).22 The FAB MS for 24-ether1-(OMe)24,including the doubly charged (M- (OCH3)2)2+ cluster ion, wasdiscussed previously.22

Gel permeation chromatography (GPC) with multiangle lightscattering (MALS) provides another absolute measure ofmolecular mass and column-dependent measure of monodis-persity (or polydispersity). The elution time is decreasing inthe order 1-(OMe)24, 1-H24, 12-(OMe)19, and 2-(OMe)8,reflecting decreasing hydrodynamic radii for the decreasingmolar masses (Figure 4). (The structure of1-H24 is shown inScheme 3.) All four compounds are monodisperse, giving PD) 1.00 for the first-order polynomial fit (Table 4s, Figure 2s,Supporting Information). The measuredMw for hydrocarbon1-H24 is 6.3-6.4 kDa, which is in an excellent agreement with

the formula mass of 6314 g mol-1. For all three polyethersMw’sare overestimated by about 10% (Table 4s, Supporting Informa-tion); assuming that only about 90% of the injected mass ofpolyether is eluted into detectors, good agreement with theformula masses is obtained. Such partial retention on thetetrahydrofuran-eluted GPC column is reasonable in view ofthe relatively high reactivity of triarylmethyl ethers.

1H and 13C NMR spectra corroborate the expected 4-foldsymmetry for 24-ether1-(OMe)24 and 8-ether2-(OMe)8.33 TheNMR spectra for dendritic fragments of polyethers1-(OMe)24,8-H, and10 are best interpreted in terms of two nonequivalentsets of 4-tert-butylphenyl groups, analogously to the previouslydiscussed NMR spectra of branch module8.21,33aIn the aromaticregion of the1H NMR spectra for 24-ether1-(OMe)24 at 348K, the expected COSY off-diagonal peaks are observed, exceptfor the two most downfield, broadened resonances at 7.97 (4H)and 7.90 (8H).22 In the aromatic region the of1H-13C HMQCspectrum at 348 K, 9 out of 10 expected (assuming insufficient

(33) (a) In thet-Bu region of1-(OMe)24, the1H NMR spectrum at 293 K showsthree singlets in the expected ratio (16:16:4); at 348 K, the1H and 13Cresonances for the diastereotopict-Bu groups are not resolved. (b) In theMeO-group region of1-(OMe)24, three (1:1:4)1H resonances are resolvedat 293 K.

Figure 3. Molecular conformation (two views) for macrocyclic tetraether7E as determined by a single-crystal X-ray crystallography. The hydrogen atomsand molecules of solvent of crystallization (benzene) are not shown. Carbon, bromine, and oxygen atoms are depicted with ellipsoids representing the 50%probability level.

Chart 1. Structures of Side Products in Synthesis of 1-(OMe)24

and 2-(OMe)8

Figure 4. Gel permeation chromatography of1-(OMe)24, 1-H24, 12-(OMe)19, and2-(OMe)8. Only plots from the refractive index detector areshown.



resolution for diastereotopic 4-tert-butylphenyls) cross-peaks areobserved; in particular, the1H resonance at 7.90 ppm correlatesto a broad13C resonance at 127.0 ppm (Figure 5). The absenceof the cross-peak to the1H resonance at 7.97 ppm correspondsto the missing nonquaternary13C resonance in the aromaticregion, which is perhaps too broad to be detected under thepresent experimental conditions.

In the less sterically congested octaether2-(OMe)8, the mostdownfield1H resonances appear at similar chemical shifts, 8.06(4H) and 7.95 (8H), and do show off-diagonal peaks in theCOSY correlation at ambient temperature (Figure 3s, SupportingInformation). Similarly, both downfield1H resonances showcross-peaks in the1H-13C HSQC correlation at ambienttemperature, i.e., (8.06, 130.4) and (7.95, 127.5) (Figure 4s,Supporting Information). Therefore, the two most downfield1H

resonances in1-(OMe)24 are assigned to the four 1,3,5-trisubstituted benzene rings of the calix[4]arene core.

2. Generation of Carbopolyanions and Polyradicals.Thegeneration of carbopolyanions and polyradicals is shown inScheme 3. When polyethers1-(OMe)24 and 2-(OMe)8(0.5-30 mg) are treated with Na/K alloy in THF-d8 (0.06-0.12 mL), the reaction mixture briefly turns blue and, subse-quently, deep purple red or purple blue. After about 5 days at283 K, the solutions of deep purple red carbopolyanion124-

and purple blue carbooctaanion28- are filtered into a SQUID,NMR, ESR, or SANS sample container (Figure 13). Additionof iodine in small portions at 170-167 K leads to a blue, green(or blue gray), and, finally, yellow-brown to red-brown reactionmixture to give polyradicals1 and2 (Scheme 3).34

Unlike previously studied low molecular weight carbopolya-nions, which typically possessed well-resolved NMR spectra,7,34a,35

124- has broadened1H NMR spectra in the 293-193 K range,preventing peak assignment. The broadening of the resonancesis reversible and increases significantly at low temperatures.(The solutions of124- appear as more viscous compared to thesolutions of the corresponding 24-ether1-(OMe)24 and 24-radical1.) The13C NMR spectrum at 293 K shows fewer thanexpected, relatively broad resonances (Figure 6).

The13C resonance at 85.8 ppm is in the chemical shift rangeof the triarylmethyl carbons in analogous carbopolyanions.34a,35

Moreover, no resonances corresponding to methoxy carbons aredetected. Addition of MeOH to carbopolyanion124- gives theisomeric mixture of the corresponding hydrocarbon1-H24.Similarly, hydrocarbon2-H8 is obtained, when octaradical2 istreated with Na/K alloy at 178-195 K, and then the resultantcarbopolyanion is quenched with MeOH.

FAB MS for poly(arylmethyl) hydrocarbons are relativelydifficult to obtain, compared to the corresponding polyethers.21

The expected molecular ion for2-H8 is detected with the signal-to-noise of only 2-3, and for much larger1-H24, no molecularion is found in FAB MS. However, GPC MALS of1-H24 inTHF gives values ofMw that are in excellent agreement withthe formula molecular mass. Furthermore, molecular size asmeasured by radius of gyration (see section on SANS studies)for 1-H24 is similar to that for 24-ether1-(OMe)24. The1H NMRintegrations of the aromatic, Ar3CH, andtert-butyl regions arein good agreement with the expected ratio of 196:24:324 forhydrocarbon1-H24; the13C NMR spectrum shows the expectedresonances for Ar3CH in the 56-57 ppm region. Both NMRand IR spectra indicate the absence of the arylmethyl etherlinkages.

3. Magnetic Studies of Polyradicals. 3.1. ESR Spectros-copy.The CW X-band ESR spectrum of octaradical2 in THF-d8/2-methyltetrahydrofuran at 77 K shows only one unresolvedresonance in both∆ms ) 1 and∆ms ) 2 regions. It is expectedthat the spectrum possesses too many closely spaced lines tobe resolved. The∆ms ) 1 region for the previously studied1,3-phenylene-based octaradical also showed a broad resonance,and only 12 (out of expected 16) barely resolved shoulders havebeen tentatively assigned to theS ) 4 ground state with axialzero field splitting parameter|D/hc| ≈ 0.001 27 cm-1.7 The

(34) (a) Rajca, A.J. Am. Chem. Soc.1990, 112, 5889-5890. (b) Rajca, A.J.Am. Chem. Soc.1990, 112, 5890-5892.

(35) NMR spectroscopy of triarylmethyl-based carbopolyanions: (a) Utama-panya, S.; Rajca, A.J. Am. Chem. Soc.1991, 113, 9242-9251. (b) Rajca,A.; Utamapanya, S.J. Org. Chem.1992, 57, 1760-1767.

Scheme 3. a Generation of Polyradicals 1 and 2

a Conditions: (i) Na/K, 283 K for∼5 d; (ii) I2, 167-170 K; (iii) MeOH;(iv) Na/K, 178-195 K for several hours.

Figure 5. 13C NMR (125 MHz, benzene-d6) spectrum for 24-ether1-(OMe)24 at 348 K. Main plot: full spectrum. Inset plot:1H-13C HMQCcorrelation in the aromatic region.



presence of the biphenylene moieties in2 is expected toincreased delocalization of spin density in2 compared to the1,3-phenylene-based octaradical.6 This suggests relatively smallvalues of the predominant magnetic dipole-based contributionto |D/hc|.20,21,36-38 Consequently, the ESR resonances in theS) 4 state of2 may be about 2-3 times more densely spacedwithin the spectral width of 14|D/hc|, leading to an unresolvedspectrum. In addition, the thermal population of the low-spinexcited states (see bulk magnetization and magnetic susceptibil-ity studies) may further complicate the ESR spectrum at 77 K.Because the spectral width is approximately constant within thehomologous series of poly(arylmethyls), resonances in the CWESR spectra become rapidly more congested with increasingvalues of S (number of resonances increases as 4S or 6Sdepending on symmetry). Therefore, bulk magnetic susceptibil-ity and magnetization studies are techniques of choice fordetermination of large values ofS.39,40

3.2. Bulk Magnetic Susceptibility and MagnetizationStudies.For magnetic studies, samples of polyradicals1 and2are typically prepared from 0.5 to 1.8 mg of polyethers1-(OMe)24 and2-(OMe)8 in THF-d8 (0.06-0.08 mL). Specialcare is taken to ensure accurate weight for the polyethers.41

Magnetization (M) is measured as a function of magnetic field(H ) 0-50 kOe) and temperature (T ) 1.8-150 K) for 1 and2 in THF-d8. For selected samples, the following sequences ofmeasurements is carried out: first, without annealing (withsample chamber degassed at 90 K); second, with prior annealingat 170 K (slightly above the melting point of the matrix); third,after exposure of the sample to room temperature for about0.5 h.

For the most dilute samples of1 (∼0.002 M) and2 (<0.005M), the M vs H data at 1.8, 3, 5, and 10 K are numerically fitto one Brillouin function (B(S)),42 with spin (S) and magnetiza-tion at saturation (Msat) as variable parameters (Tables 1 and2). The values ofS ) 9.8 andS ) 3.8 are obtained for1 and

2; theM/Msat vs H/T plots are nearly overlapping with theS)10 andS ) 4 Brillouin functions, respectively (Figure 7). Theobserved temperature dependence ofSis consistent with an idealparamagnet behavior for dilute samples of1 and2 below 5 K.For more concentrated samples of1 and2, the additional mean-field parameters (Θ) are used to correct for small intermolecularantiferromagnetic (Θ < 0) interactions. Numerical fits tomodified Brillouin functions,M vsH/(T - Θ), with Θ ) -0.03or -0.05 K, giveS) 10.0 at 1.8, 3, and 5 K andS) 9.8 at 10K for 1. For 2, S ) 3.6 (|Θ| ) 0.1-0.2 K) at 1.8, 3, and 5 Kare obtained (Tables 1 and 2).43

Additional numerical fits of theM vs H data for1 are car-ried out with linear combination of two Brillouin functions,B(S) andB(1/2), using three variable parameters:S, Msat, andw (eq 1).

(36) The zero field splitting parameter (|D|) vs the interdipole distance indiradicals: Rohde, O.; Van, S. P.; Kester, W. R.; Griffith, O. H.J. Am.Chem. Soc.1974, 96, 5311-5318.

(37) The values of|D/hc| (cm-1) for 3,4′-biphenylene-based di-, tri-, andpentaradicals are smaller by a factor of about 2-3, compared to their 1,3-phenylene counterparts, e.g., for 3,4-′biphenylene- vs 1,3-phenylene-basedpolyradicals:20,21 0.0025 vs 0.0066 (diradicals); 0.0016 vs 0.004-0.006(triradicals); 0.0016 vs 0.0027 (pentaradicals).

(38) Minato, M.; Lahti, P. M.; van Willigen, H.J. Am. Chem. Soc.1993, 115,4532-4539.

(39) Rajca, A.; Utamapanya, S.; Thayumanavan, S.J. Am. Chem. Soc.1992,114, 1884-1885.

(40) In the most favorable case of the|E/hc|, polyradical withS ) 12 wouldpossess 48 resonances in the∆ms ) 1 region; with the expected spectralwidth of the order of 0.006 cm-1, only a broad single line would beobserved. The spectral width, due to the magnetic dipole-dipole couplings,may be significantly greater (elongated or flat shapes) or smaller (spherical-like shapes) than 0.006 cm-1.

(41) (a) The weighed amount of polyether must be viewed as an upper boundfor the actual amount used for generation of polyradical because of thedifficulty in quantitative transfer of electrostatic powder in to the reactionvessel. (b) One sample of2 is prepared on a 9.4-mg scale for SQUID-measurement-followed-by-quenching experiment (Table 2, entry 1).

(42) Carlin, R. L.Magnetochemistry; Springer: Berlin, 1986.(43) The mean-field correction with parameterΘ, as implemented here, provides

an approximate description of small exchange couplings, in particularintermolecular antiferromagnetic couplings in more concentrated solutions.Such a description is valid as long as|Θ| is relatively small compared tothe studied temperature range. The origin of the large value of|Θ| ) 0.25K, shown by one sample of1 after annealing at 170 K (Table 1, entry 1),is not known. The increased values of|Θ| for the lower molecular weightpolyradicals (2 vs 1) follow the previously observed trends (e.g., ref 21).

Figure 6. 13C NMR (125 MHz, THF-d8) spectrum for carbopolyanion124-. Exponential line broadenings of 10 and 1 Hz are applied to the downfield(relative scale of 12) and upfield (relative scale of 1) parts of the spectrum, respectively.

Table 1. Summary of Magnetic Data for 24-Radical 1

One-Brillouin Two-Brillouinsamplelabel

mass(mg)

anneal(K) S −Θ (K) Ss −Θ (K) Msat

a (µB) øTmaxb J/k (K)

1087c 1.50 90 10.0 0.03 0.70 46.6 6.6d

170 10.5 0.3 0.71 6.5d

293 2.8 0.25 0.18 3.81109 1.26 90 9.8 0 9.9 0 0.54 35.8 6.9d

170 9.8 0 0.53 35.4 7.1d

1756 1.54 90 10.0 0.05 10.0 0.05 0.63 43.0 7.3e

170 10.0 0.05 10.1 0.05 0.63 44.6 7.7e

293 3.3 0.1 3.3 0.1 0.24 6.21911f 0.50 90 8.2 0 0.46 26.6 7.5e

1923 1.13 170 9.6 0.1 9.7 0.1 0.60 38.3 7.2e

a Msat/mol of triarylmethyl ether.b øTmax/mol of 24-ether1-(OMe)24.c Point-by-point correction for diamagnetism, except for samples 1911 and1923.d At 5000 Oe.e At 500 Oe.f Polyradical preparation atT > 170 K.



TheS) 1/2 Brillouin function (B(1/2)) may account for someof the polydispersity in the value ofS. Parameterw is a measureof relative contribution from different Brillouin functions tooverall M. Taking into account that contribution to overallMfrom each Brillouin function has to be effectively multipliedby its value ofS,42 w is dependent on another variable parameterS, as well. Consequently, values of spin-weighed average spin(Ss) are calculated using the following expression:Ss ) (S +0.5w)/(1 + w). Addition of the third variable parametersomewhat improves the numerical fits, though the values ofSs

are very similar to the values ofSobtained from one-Brillouinfits (Table 1). This may suggest that the amount of theimpurities, with very low values ofS, is relatively insignificant.44

TheM vs T data atH ) 5000, 500, and 50 Oe are plotted asthe product of magnetic susceptibility per mol of startingpolyether (ø ) M/H) and temperature vs temperature, i.e.,øTvsT (Figure 8). For both1 and2, the values oføT are increasingwith decreasing temperature, indicating the thermal depopulationof the low spin excited states, i.e., suggesting the presence of a

weak ferromagnetic coupling. At low temperatures and modestmagnetic fields (H ) 5000 Oe), the downward turn inøT ispredominantly, if not exclusively, associated with the paramag-netic saturation. Ideal paramagnetic behavior (flatøT vsT plot)is established for1 at T e 5 K, using low magnetic fields (H )50 Oe) (Figure 8, inset).

The øT vs T dependence is fit to a model on the basis of apentamer of four spin carriers withS ) 5/2 (for 1) or S ) 1/2(for 2) ferromagnetically coupled to one with a spin ofS )4/2.22 Energy eigenvalues for Heisenberg Hamiltonian areobtained by vector decoupling technique.45-48 For 2, onlyrelatively concentrated solutions are used for theøT vs T fits;this provides adequate signal-to-noise, especially in the highertemperature range, where the overall magnetic moment of thesample is diamagnetic. Equations for magnetization, includingsaturation effects, are derived using standard formulas.47,48

(44) For1 at 1.8 and 2.5 K, the maximum value of the parameter dependencein the numerical fits to eq 1 does not exceed 0.91 (Table 1).

(45) Heisenberg, W.Z. Phys.1928, 49, 619-636.(46) Beloritzky, E.; Fries, P. H.J. Chim. Phys. (Paris)1993, 90, 1077-1100.(47) Rajca, A. InHyper-structured Molecules III; Sasabe, H., Ed.; Gordon and

Breach: Reading. U.K., 2001; Chapter 3, pp 46-60.(48) Rajca, A.Mol. Cryst. Liq. Cryst.1997, 305, 567-577.

Table 2. Summary of Magnetic Data for Octaradical 2

Numerical Fits

Brillouin Heisenberg Hamiltonian

sample labelc mass (mg) concn (M) anneal (K) S Msata (µB) −Θ (K) J/k (K) −Θ (K) øTmax

b (emu K mol-1)

Suk98d na <0.005 90 3.8 na 0.0 na na naSul13 1.50 0.008 90 3.6 0.77 0.2 33 0.15

170 3.6 0.76 0.2 34 0.16 7.01138 1.64 0.011 90 3.5 0.81 0.2 37 0.14 7.3Sul08e <1.8 <0.01 90 3.6 na 0.1 30 0.06 na

a Msat/mol of triarylmethyl ether.b øTmax/mol of octaether2-(OMe)8. c Point-by-point correction for diamagnetism, except for sample Sul08.d 0.009 Moctaradical2 prepared from 9.4 mg of octaether in the old-style generation vessel and then further diluted.e Preparation in glovebox.

Figure 7. SQUID magnetometry (H ) 0-50 kOe) for dilute solutions ofpolyradicals1 (0.002 M, sample label 1109) and2 (<0.005 M, samplelabel Suk98) in THF-d8. Experimental points atT ) 1.8, 3, 5, and 10 Kand Brillouin functions withS) 4, 10, and 12 are shown, as symbols andlines, respectively. Numerical fitting to Brillouin function, using two variableparameters (SandMsat), givesS) 9.8 and 3.8 for1 and2, respectively, at1.8, 3, and 5 K. At 10 K,S ) 9.6 is obtained for1. The parameterdependencies are 0.26-0.72 and 0.32-0.74 for1 and2, respectively. Allexperimental data here are plotted after point-by-point correction fordiamagnetism.

M ) Msat[(B(S) + wB(1/2))]/(1 + w) (1)

Figure 8. Plots of øT vs T for concentrated solutions of polyradicals1(0.003 M, sample label 1756) and2 (0.008 M, sample label Sul13) in THF-d8. The symbols and lines are the experimental points and numerical fits tothe spin-pentamer models, respectively. For1 at H ) 500 Oe, the fittingparameters and their parameter dependencies areJ/k ) 7.7 K (0.46) andN) 1.16 × 10-7 mol (0.46); for2 at 5000 Oe,J/k ) 33.8 K (0.59),N )4.17 × 10-7 mol (0.76), andΘ ) -0.16 K (0.62) are obtained. Allexperimental data here are obtained after annealing at 170 K and point-by-point correction for diamagnetism.



Numerical fits useJ/k (spin coupling constant in Kelvin) andN (number of moles of polyradical), as variable parameters.J/k) 7 ( 1 K andJ/k ) 34 ( 4 K, corresponding to a pairwiseferromagnetic couplings of spins 5/2 to 4/2 and 1/2 to 4/2,respectively, through 3,4′-biphenylene moiety, are obtained(Figure 8, Tables 1 and 2). For such values ofJ/k, it is calculatedthat both1 and2 should behave as ideal paramagnets atT e 5K; i.e., their S ) 12 and S ) 4 ground states are nearlycompletely populated.49 This is consistent with a flatøT vs Tplot at low magnetic fields, such as 50 Oe for1 in the inset ofFigure 8.50

Although øT vs T plots fit reasonably well to the pentamermodels for both1 and2, the values ofS from the curvatures ofBrillouin functions (M vs H/T plots) are somewhat below thetheoretical values ofS ) 12 for ferromagnetically coupled 24unpaired electrons in1 andS) 4 for ferromagnetically coupled8 unpaired electrons in2, respectively. For the quantitativevalues ofMsat and øT, based upon the amount of polyethersweighed for polyradical generation, the discrepancy betweenthe experiment and the theory is even greater. This may in partarise from incomplete transfer of samples of polyethers, whichare highly electrostatic powders, to the reaction vessel, masslosses at the stage of filtration of carbopolyanion, or chemicaldefects in generation of polyradicals.

For quantitative conversion of polyethers to ferromagneticallycoupled polyradicals1 and 2, øTmax should reach 78 and 10emu K mol-1, respectively. However, the maximum values oføT are only about 45 and 7 emu K mol-1 for 1 and 2,respectively.

Msatmeasures the number of unpaired electron spins (or spinconcentration) in the limit of low temperature and high magneticfield. For the best samples of1, Msat is about 0.6-0.7µB/arylmethyl; i.e., 60-70% of the expected value for quantita-tive conversion of1-(OMe)24 to 1 with 24 unpaired electrons.Analogous percentages for2 are somewhat higher at about 80%.The values ofMsat for 1 imply that only 14-17 electron spinsare effectively present in an average molecule of1 within thelimit of low T and highH. How could this relatively smallnumber of radicals (S ) 1/2) lead to relatively high value ofS) 10 for1? Analogous question arises for2. Such discrepanciesmay in principle be reconciled, considering that bothMsat andS are different averages for polydisperse spin systems.Msat

corresponds to a number average;S, as fit to the curvature ofthe Brillouin function, is approximately a weighed average (Ss).51

For polydisperse systems, weighed average may be significantlygreater than the corresponding number average. Furthermore,Msat may be underestimated by incomplete mass balance, asmentioned in the preceding paragraphs.41a

In the preliminary report, only qualitative magnetic data for1 were available.22 The discrepancy between the theoreticalvalue ofS) 12 and the experimental value ofS) 10, obtainedfrom the curvature of the Brillouin plot, was ascribed to thepresence of small and randomly distributed density of chemical

defects.22 The corresponding percolation model (ExperimentalSection) gives density of chemical defects at the level of about2%.22,51Such defects may result from less than 100% yield forgeneration of “unpaired” electrons or synthetic impurities inpolyether precursors. However,Msat ) 0.6-0.7 µB wouldcorrespond to the density of chemical defects in the 30-40%range; this would imply highly nonstatistical (rather thanrandom) distribution of chemical defects, with the predominantdensity of defects at the 16 terminal triarylmethyl sites. Becauseof low temperatures employed for measurement ofMsat,antiferromagnetic interactions may contribute to the low valuesof Msat. For example, antiferromagnetic exchange couplingarising from a near 90° twisting of one of the biphenyls (at thephenyl-phenyl CC bond) would lead to cancellation of 10electron spins; i.e.,Msat ) 14 µB/24 ≈ 0.58 µB and S ) 7.Analogously, two such twistings, would give polyradical withMsat ) 4 µB/24 ≈ 0.17µB andS) 2. A mixture of conformerswith 0, 1, and more twistings could qualitatively account forthe experimentally found averages forMsat andS.52

Thermal Stability (Persistence) of Polyradical 1.Annealingat 170 K (just above the melting point of the matrix) for a fewminutes does not affect the results for two samples of1;however, the third sample shows increased values ofSand|Θ|after after annealing (Table 1). For two samples, magneticmoment is continuously measured at 170 K for 12+ h. Thesample, which is somewhat overtitrated with iodine, shows aslow decrease of moment over time. However, the other samplepossesses unchanged magnetic moment after 12+ h at 170 K,suggesting that polyradical1 is persistent (stable) at 170 K. Twosamples of1 are annealed at room temperature for 30 min, andsubsequently, repeat magnetic studies are carried out (Table 1).For both samples, the values ofS≈ 3 are obtained, i.e., about30% of the original value. Similar relative decreases areobserved for values ofMsat (Table 1).

Conformational Searches. Monte Carlo conformationalsearches for polyradical1 provided low-energy conformationswith elongated shapes with overall dimensions of 4× 3 × 2nm (Figure 9). As shown by the color coding for polyradical1in Figure 9, the core calix[4]arene adopts a 1,3-alternateconformation. Consequently, each pair of the diagonally posi-tioned dendritic branches occupies the opposite faces of the corecalix[4]arene. The conformation of polyradical1 has an ap-proximateD2d symmetry; the two pairs diagonally positioneddendritic branches are interchangeable by theS4 axis, collinearwith the C2 axis of the molecule (Figure 9).

Monte Carlo conformational searches for tetraradical3 givethe analogous 1,3-alternate conformations for the lowest energystructures. In3, the eight CCCC torsional angles along the innermacrocyclic carbon backbone of the calix[4]arene core aremoderate, at about 47°, consistent with theS) 2 ground statefound in THF (or 2-MeTHF/THF) matrixes.7 However, in1,the analogous torsional angles are in the 40-70° range, e.g.,63, 47, 72, 42, 55, 49, 67, and 49°. Such conformations should

(49) Equations forM(T,H) derived from Heisenberg Hamiltonians for the spinpentamers are used.

(50) The energy gaps between the ground state and the lowest excited state areidentical in units ofJ/k for both spin pentamers, i.e., 4J/k. The overallspan of energy levels is 20J/k (680 K) and 84J/k (588 K) for pentamerscorresponding to1 and2, respectively. For reliable calculation of thermalbehavior, all energy levels, including multiplicities andms sublevels, shouldbe taken into account.

(51) Number averageSn in refs 2 and 22 should be replaced with weighedaverageSs.

(52) A percolation model for1, in which random distribution of chemical defectsand random distribution of ferromagnetic vs antiferromagnetic couplingsacross the four biphenylene moieties are assumed, is developed (eq 5,Experimental Section). Analogous percolation models are described in detailin ref 28a. However, the numerical fits of theM vsH/T data to such modelsare not satisfactory. Possibly, steric congestion of the dendritic branchesin 1, as found in conformational searches, affects the distribution ofconformations, leading to nonrandom distribution of exchange couplingsacross biphenylene coupling units.



still be compatible with the ferromagnetic coupling for the fourunpaired electrons in the macrocyclic core of1.10,53

The torsional angles, involving 1,3-phenylene moieties withinthe dendritic branches, are in the 20-57° range; however, thehigher angles (e.g., above 47°) are found only at the peripheryof the dendritic branch. The torsional angles for the biphenylmoieties in1 are typically about 48° for the lowest energyconformations. However, conformations, in which one of thebiphenyls has a torsional angle approaching 90°, are at∼8 kcal/mol relative to the lowest energy conformations. Severe twistingof the biphenyl moiety does not appear to affect significantlythe overall molecular shape of1.

Conclusions about the exchange coupling based upon calcu-lated conformations must take into consideration that it is notabsolutely certain whether the conformation associated with theglobal minimum was found and whether the calculated confor-mations in the gas phase represent adequately those in THF-d8

frozen solutions.54 With these precautions in mind, the lowestenergy conformations of1 are probably compatible withferromagnetic coupling; the somewhat higher in energy con-formations may have antiferromagnetic coupling between thedendritic branch and the macrocyclic core.

The calculated, dumbbell-like molecular shapes for1 haveoverall sizes exceeding 1 nm making possible their experimentalverification using small-angle scattering techniques.55

Small-Angle Neutron Scattering.Solutions of polyradical1, 24-ether1-(OMe)24, hydrocarbon1-H24, and carbopolyanion124- in THF-d8 are studied with small-angle neutron scattering(SANS).

Polyradical1 is handled at temperaturese170 K at all timesto prevent any substantial decomposition. This poses technicalproblems for obtaining the SANS data of high quality: (1)

formation of frozen moisture or frozen organic solvent on theoutside wall of the sample cell; (2) incomplete melting of thefrozen sample solution or inadvertent particles (e.g., precipitate)inside the sample cell. Either of these two problems will leadto an excess of SANS intensity, especially in the low-q range.Elaborate procedures for the sample preparation and handlingare developed as described in the Supporting Information.

The logarithmic plots of SANS intensity (I) vs momentumtransfer (q) for polyradical1, 24-ether1-(OMe)24, and hydro-carbon1-H24 are shown in Figures 10-12. The numerical fitsto the SANS data are obtained using the simulated annealingapproach of Svergun, as implemented in GNOM/DAMMINsoftware packages.56,57 Representative reconstructions of low-resolution particle shapes in the insets of Figures 10-12 are

(53) For each 1,3-phenylene moiety of the macrocyclic core of1, at most onetorsional angle is relatively large near 70°, with the other torsional angleapproaching 50°. Severe twisting on one side of 1,3-phenylene moiety doesnot appear to lead to antiferromagnetic coupling, e.g., ref 10.

(54) There is no detailed quantitative data on the dependence of the exchangecoupling vs torsional angles in either 1,3-phenylene or 3,4′-biphenylenemoieties. However, a “Karplus-Conroy-type” relationship for exchangecoupling in trimethylene-based bis(semiquinone) diradicals was proposed:Shultz, D. A.; Fico, R. M., Jr.; Bodnar, S. H.; Kumar, K.; Vostrikova, K.E.; Kampf, J. W.; Boyle, P. D.J. Am. Chem. Soc.2003, 125, 11761-11771.

(55) Roe, R. J.Methods of X-ray and Neutron Scattering in Polymer Science;Oxford University: New York, 2000; Chapter 5.

Figure 9. Low-energy conformation for polyradical1 that is obtained usingMonte Carlo conformational searches with the MM2* force field (Macro-model 6.5).

Figure 10. Main plot: SANS intensity (I) vs momentum transfer (q )0.049-0.419 Å-1) for 9 × 10-4 M polyradical1 (sample label 1907) inTHF-d8 at 170 K. The symbols and solid line correspond to the experimentaldata points and the numerical fit using GNOM/DAMMIN simulatedannealing (ø ) 4.712), respectively. Inset: Low-resolution particle shapereconstruction for1 obtained from the GNOM/DAMMIN fit. Two side views(rotated by 90°), using both the DAMMIN spheres and the sphericalharmonics-based envelopes, are shown.

Figure 11. Main plot: SANS intensity (I) vs momentum transfer (q )0.012-0.534 Å-1) for 1.6 × 10-3 M 24-ether1-(OMe)24 in THF-d8 atroom temperature. The symbols and solid line correspond to the experi-mental data points and the numerical fit using GNOM/DAMMIN simulatedannealing (ø ) 1.020), respectively. Inset: Low-resolution particle shapereconstruction for1-(OMe)24 obtained from the GNOM/DAMMIN fit. Twoside views (rotated by 90°), using both the DAMMIN spheres and thespherical harmonics-based envelopes, are shown.



illustrated using both DAMMIN spheres and spherical harmon-ics envelopes (up to 6th order); two orientations, related byrotation of about 90° with the respect to the long axis of themolecule, are shown. The spherical harmonics are employedto smooth out the excessive detail of the DAMMIN shapes.58

The radii of gyration (Rg) for these shapes are 1.5 nm (for1)and 1.4 nm (for1-(OMe)24 and1-H24). Guinier law analysis,59

which does not consider any particular shape, gives identicalvalues of Rg for 1-(OMe)24 and 1-H24. For 1, Guinier lawanalysis is not carried because of excess ofI, especially in thelow-q range. The cause for this excess ofI in all samples of1is not known. However, this excess ofI leads to large values ofø2 in the DAMMIN fits, though the information concerningmolecular shape is contained primarily at the relatively high-qvalues.60

Overall shapes for1, 1-(OMe)24, and 1-H24 have somesimilarity to a dumbbell (large on the top and the bottom withthe narrow middle part). The experimental resolution of theSANS experiment hardly allows for more detailed descriptionof the reconstructed shape.60,61Such a general “dumbbell-like”description also applies to the lowest energy conformations of1 found by conformational searches (Figure 9).

One of the samples of1 is allowed to attain room temperaturefor about 4 min. Following cleaning of outside windows of thesample cell at room temperature, the sample is reinserted tothe cryostat and the SANS data are collected at 170 K again.The excess ofI is still visible at low-q values, and moreimportantly, the molecular shapes are now qualitatively different,suggesting decomposition of1 (Figure 5s, Supporting Informa-tion).62

SANS data for carbopolyanion124- in THF-d8 are obtainedat room temperature and 170 K (Figure 6s, Supporting Informa-tion). However, DAMMIN-based shape reconstructions for124-

may not be reliable because of high dependence of the obtainedshapes on the applied constraints. Overall, the shapes for124-

might be significantly different and of greater size comparedto 1 and/or124- forms aggregates. The possibility of aggregationis supported by the observation of highly viscous solutions of124- in THF-d8 at low temperatures (e.g., 170 K) and apparentincrease inRg with extending theRgq range of the Guinier lawanalysis.

Magnetic Shape Anisotropy. The possible shapes forpolyradical1, which are obtained from conformational searchesand SANS-based shape reconstructions, may be viewed aselongated. The simplest approximations for such a shape, forwhich demagnetizing factors are readily calculated, are ellipsoidsof rotation, e.g., a prolate ellipsoid.63 In such a case, the barrierfor coherent rotation of magnetization (EA) arising from theshape anisotropy is described by eq 2, where∆N, Is, andV arethe difference of demagnetizing factors between the two longestsemiaxes of ellipsoid, magnetization at saturation (per unitvolume), and volume of the ellipsoid, respectively.4,5,27,64a

Using a prolate ellipsoid (anisometry,a/b ) 2) of volumeand spin density similar to that of1, the shape anisotropy barrier

(56) (a) GNOM: Svergun, D. I.J. Appl. Crystallogr.1992, 25, 495-503. (b)DAMMIN: Svergun, D. I.Biophys. J.1999, 76, 2879-2886. (c) Svergun,D. I. J. Appl. Crystallogr.2000, 33, 530-534. (d) Svergun, D. I.; Stuhrman,H. B. Acta Crystallogr., Sect. A1991, 47, 736-744.

(57) Several approaches to reconstruction of three-dimensional solution structuresof macromolecules (proteins) from one-dimensional small-angle scatteringdata are available; however, the ab initio approach, based upon Svergun’ssimulated annealing GNOM/DAMMIN programs, appears to give the bestresults, e.g.: Zipper, P.; Durchschlag, H.J. Appl. Crystallogr.2003, 36,509-514.

(58) CRYSOL: Svergun, D. I.; Barberato, C.; Koch, M. H. J.J. Appl.Crystallogr.1995, 28, 768-773.

(59) Guinier law: (a) Reference 55, pp 167-174. (b) Guinier, A.; Fournet, G.Small Angle Scattering of X-rays; Wiley: New York, 1955.

(60) Resolution of SANS scales with 2π/q.(61) Because the shapes in this size range close to 1 nm is determined at

relatively highq, there is a possibility for the interference from the internalstructure and the solvent structure. For1, the excess ofI, which is foundat low q, may tail into the high-q region, leading to further decrease inreliability of the shape reconstruction.

(62) After cleaning of the external windows of the sample cell for1 at roomtemperature, the excess ofI was still present at 170 K. However, the colorof the sample is too dark to see whether the precipitate is present after 4min at room temperature. After longer times, the color fades and precipitatebecomes clearly visible.

(63) (a) Demagnetizing factors for ellipsoids: Osborn, J. A.Phys. ReV. 1945,67, 351-357. (b) Stoner, E. C.Philos. Mag.1945, 36, 803-821. (c)Inversion of magnetization in single-domain ellipsoids: Stoner, E. C.;Wohlfarth, E. P.Philos. Trans. R. Soc. London1948, A240, 599-642.Reprinted in: IEEE Trans. Magn.1991, 27, 3475-3518.

(64) (a) In eq 2, magnetization at saturation is defined byIs rather thanMsat(defined in the preceding sections) according to typical notation. (b) Foran ellipsoid withnel ferromagnetically coupled electron spins (totalS )nel/2) with Is ) nelµB/V, EA in the units temperature (i.e.,EA/k, wherek isa Boltzman constant) is as follows:EA/k ) [(µB

2/k)∆N(nel/V)]S. Thus, forhomologous ellipsoids with identical shape (∆N ) constant) and withidentical spin density (nel/V ) constant),EA/k varies linearly with the valueof S. (c) For an idealized 4× 2 × 2 nm prolate ellipsoid (a/b ) 2) with24 electron spins,∆N ≈ 3.0 andnel/V ) (9/π) × 1021 electron cm-3. Thus,for this ellipsoid and homologous ellipsoids,EA/k ≈ 5S mK; for S ) 12,EA/k is approximately 60 mK. (d) The 4× 3 × 2 nm general ellipsoidmay possibly be a better approximation to the “dumbbell-like” shape of1with dimensions of 4× 3 × 2 nm. For such ellipsoid,∆N ≈ 1.2 is obtainedfrom demagnetizing factors, leading toEA/k that is significantly below 60mK (by a factor of 2-3). (e) One of the reviewers commented on a possiblerelationship between the anisotropy barriers derived from values ofD andthose obtained from demagnetizing factors. The discussion will be limitedto prolatelike shapes, in whichD < 0 arises solely from the magneticdipole-dipole interactions (couplings). For a homologous series of high-spin polyradicals (with similar spin densities and similar shapes), valuesof |D|, scale approximately as 1/S;26,40such polyradicals have approximatelyconstant ESR spectral width,|D(4S- 2)|. Therefore, the anisotropy barrierfor such polyradicals (or ellipsoids), which is related to the value of|DS2|,varies linearly with the value ofS, similarly as determined fromdemagnetizing factors in ellipsoids.64b Furthermore, if the ESR spectralwidth of 0.006 cm-1 (i.e., 4|D/hc|S≈ 0.006 cm-1) is assumed for1 withS ) 12, then the value of|DS2| is of the order of 30 mK, i.e., similar tothat obtained from demagnetizing factors.40

Figure 12. Main plot: SANS intensity (I) vs momentum transfer (q )0.012-0.549 Å-1) for 1.1× 10-3 M hydrocarbon1-H24 in THF-d8 at roomtemperature. The symbols and solid line correspond to the experimentaldata points and the numerical fit using GNOM/DAMMIN simulatedannealing (ø ) 1.109), respectively. Inset: Low-resolution particle shapereconstruction for1-H24 obtained from the GNOM/DAMMIN fit. Two sideviews (rotated by 90°), using both the DAMMIN spheres and the sphericalharmonics-based envelopes, are shown.

EA ) (∆NIs2V)/2 (2)



for inversion of magnetization of about 60 mK is predicted.64

This estimate should be viewed as an upper bound.64 Such alow barrier is consistent with the paramagnetic behavior of1at 1.8 K and above. However, for homologous prolate ellipsoidswith a/b ≈ 2 (and same spin density), the shape anisotropybarrier scales as 5SmK;64 i.e., for macromolecules with valuesof Sof the order of several thousands (and spin density similarto that of 1), the magnetization may become blocked at thereadily accessible temperatures of the order of 10 K.

Conclusion

Quantitative magnetic measurements on dendritic-macrocyclicpolyradical1 and its lower homologue2 confirm the presenceof high-spin ground states. The detailed interpretation of thethese measurements is complicated by the possible presence ofconformations with different exchange couplings, different typesof averages for the measured quantities (S, Msat, andøT), andthe possibility of incomplete mass transfers. Molecular sizesand shapes for1 obtained from conformational searches showfair agreement with the shape reconstructions derived from theSANS experiments.

Polyradical1 with averageS ) 10 may be viewed as ananometer-sized organic spin cluster, for which estimated shapeanisotropy barrier for inversion of magnetization is rather small,in the miliKelvin range. Because the shape anisotropy barriersmay scale withS, significant barriers for inversion of magne-tization in macromolecules with averageS ) 103-104 andelongated shapes may be found. The shape anisotropy may inpart be responsible for blocking of magnetization in the recentlyreported organic polymer with averageS ≈ 5000.1

Experimental Section

Addition of Small Volumes of Reagents.Reagent volumes of lessthan 0.3 mL (e.g., of solutions oft-BuLi, ZnCl2, etc.), encountered inmicromolar-scale syntheses, were added by counting drops of thereagent solution. Typically, the volumes were calibrated by countingnumber of drops in 0.4 mL of the reagent solution that was dispensedusing 1-mL syringe with a 22-gauge stainless steel needle. Care wastaken to mimic the conditions of the actual reaction (rate of addition,position of the needle, temperature, etc.) as closely as possible, usingthe identical 22-gauge needle.

X-ray Crystallography for 7E. The data were collected on a BrukerSMART system at the University of Minnesota. A colorless, clearcrystal (approximate dimensions 0.185× 0.105× 0.050 mm3), whichwas obtained from benzene/methanol solution by slow evaporation, wasselected for analysis. Two solvent molecules (benzene) were found fromtheE-map and refined using restraints for the thermal parameter in thebond direction (DELU). Another 1.3 benzene molecules found wereheavily disordered in a void and could not be refined to a satisfactoryresult. An investigation of the void space in the structure, excludingthe disordered 1.3 benzene molecules from the refinement, showed that107 electrons are located in a major void of approximately 640 Å3.(Each benzene molecule occupies 116 Å3 with 42 electrons.) The datasetwas corrected for disordered solvent using the program PLATON/SQUEEZE.65 The refinement using the corrected data improved theoverall structure and theR-value by 0.015. However, as the exactamount of solvent is not known, selected values below (and the CIFfile deposited on the Web) are incorrect, e.g., formula, formula weight,F(000). Crystal data for7E were as follows: C84H88Br4O4, M )1481.18, triclinic,a ) 16.249(2) Å,b ) 16.659(2) Å,c ) 16.959(2)Å, R ) 90.301(2)°, â ) 108.949(2)°, γ ) 107.420(2)°, V ) 4115.9(6)

Å3, T ) 173(2) K, space groupP1h, Z ) 2, Mo KR (λ ) 0.710 73 Å).The structure was solved by direct methods and refined by full-matrixleast-squares onF2. A total of 14 492 reflections were observed, and8206 reflections withI > 2σ(I) were recorded. Refinement statisticswith 852 parameters was as follows: wR) 0.0847 (I > 2σ(I)), R )0.0415 (I > 2σ(I)), GOF ) 0.968.

Tetrabromocalix[4]arene Diols 6. t-BuLi (13.20 mL of 1.5 Msolution in pentane, 19.80 mmol, 4 equiv) was added to a solution oftetrabromo ether4 (3.195 g, 4.946 mmol) in THF (500 mL) at-78 °Cover the period of about 10 min. After 2-3 h, a solution of diketone5 (4.000 g, 4.946 mmol) in THF (200 mL) was cannulated to thereaction mixture at-78 °C. The reaction mixture was allowed to warmto ambient temperature for 2 days. Two such reaction mixtures wereworked up with water (500 mL) and ether (300+ 200 mL). Thecombined organic layer was dried over MgSO4 and then concentratedin vacuo to give the light yellow glassy solid (or light yellow oil).Column chromatography (TLC grade silica gel, 2-10% ether in hexane)gave four fractions (in order of increasing polarity) corresponding tothe following isomers:6A (2.19 g, 17%), mixture of6B,C (1.06 g,3.5:1, 8%),6D (0.604 g, 5%), and6E (0.489 g, 4%) as white solids.Small amounts of isomers6B,C were further separated (columnchromatography or preparative TLC) for spectroscopic characterization.Another set of two reactions on identical scales gave the followingresults: 6A (1.778 g, 14%), mixture of6B,C (2.312 g, 2.5:1, 18%),6D (1.276 g, 10%), and6E (0.536 g, 4%). The calculated isotopicintensities for the most intense ions in FABMS of6A-E are asfollows: C69H69O3Br4 at (M - OCH3)+, 1261.2 (15), 1262.2 (11),1263.2 (61), 1264.2 (45), 1265.2 (100), 1266.2 (69), 1267.2 (80), 1268.2(48), 1269.2 (30), 1270.2 (15); C70H71O3Br4 at (M - OH)+, 1275.2(15), 1276.2 (11), 1277.2 (61), 1278.2 (45), 1279.2 (100), 1280.2 (70),1281.2 (80), 1282.2 (49), 1283.2 (31), 1284.2 (15), 1285.2 (5).

Diol 6A. The product was softened at 150°C and melted and becamea yellow liquid at 158-160°C. Anal. Calcd for C70H72O4Br4: C, 64.83;H, 5.60. Found: 64.96; H, 4.86. FABMS (3-NBA) clusterm/z (% RAfor m/z ) 200-1400): at (M- OCH3)+, 1261.3 (28), 1262.3 (28),1263.3 (73), 1264.3 (56), 1265.3 (100), 1266.3 (66), 1267.3 (74), 1268.3(44), 1269.3 (31), 1270.3 (14); at (M- OH)+, 1275.4 (24), 1276.4(20), 1277.4 (66), 1278.4 (55), 1279.3 (100), 1280.4 (68), 1281.4 (77),1282.4 (46), 1283.3 (32), 1284.3 (18).1H NMR (500 MHz, EM )-0.61, GB ) 0.47, CDCl3, 1H-1H COSY cross-peaks in aromaticregion): 293 K, 7.557 (t,J ) 1.5, 2 H, 7.399, 6.511), 7.557 (t,J )1.5, 2 H, 7.365, 6.560), 7.399 (s, 2 H, 7.557, 6.511), 7.365 (t,J ) 1,2 H, 7.557, 6.560), 7.286 (d,J ) 8, 4 H, 6.969), 7.248 (d,J ) 8, 4 H,6.969), 6.969 (d,J ) 9, 4 H, 7.286), 6.969 (d,J ) 9, 4 H, 7.248),6.560 (s, 2 H, 7.557, 7.365), 6.511 (s, 2 H, 7.557, 7.399), 2.876 (s, 6H), 2.589 (bs, 2 H, D2O exch.), 1.326 (s, 18 H), 1.273 (s, 18 H), 1.258(s, impurity).13C NMR (125 MHz, CDCl3; 293 K): aromatic region,expected, 20 resonances, found, 20 resonances at 150.8, 150.5, 148.3,147.7, 146.4, 145.6, 141.9, 137.7, 129.5, 129.4, 129.12, 129.09, 128.7,127.26, 127.20, 126.8, 125.0, 124.8, 122.4, 122.2; aliphatic region, 86.0,81.1, 52.0, 34.51, 34.47, 31.30, 31.27, 29.7 (impurity). IR (cm-1): 3565(O-H), 3458 (O-H), 1567 (Ar), 1084 (C-O-C).

Diol 6B. The product was softened at 152°C and melted and becamea brown liquid at 187-189 °C. FABMS (3-NBA) clusterm/z (% RAfor m/z ) 200-1520): at (M- OCH3)+, 1261.1 (26), 1262.2 (24),1263.2 (73), 1264.2 (56), 1265.2 (100), 1266.2 (71), 1267.2 (73), 1268.2(48), 1269.2 (27), 1270.2 (13); at (M- OH)+, 1275.2 (20), 1276.2(18), 1277.2 (64), 1278.2 (48), 1279.2 (94), 1280.2 (64), 1281.2 (72),1282.2 (42), 1283.2 (28), 1284.3 (14).1H NMR (500 MHz, EM )-0.59, GB ) 0.48, CDCl3, 1H-1H COSY cross-peaks in aromaticregion; 293 K): 7.560 (s, 2 H, 7.518, 6.389), 7.518 (s, 2 H, 7.560,6.389), 7.434 (s, 2 H, 7.270, 6.914), 7.299 (d,J ) 9, 2 H, 7.036),7.278 (d,J ) 9, 4 H, 6.977), 7.278 (d,J ) 9, 2 H, 6.938), 7.270 (s, 2H, 7.434, 6.914), 7.036 (d,J ) 8, 2 H, 7.299), 6.977 (d,J ) 8, 4 H,7.278), 6.938 (d,J ) 8, 2 H, 7.278), 6.914 (s, 2 H, 7.434, 7.270),6.389 (s, 2 H, 7.560, 7.518), 2.885 (s, 6 H), 2.829 (s, 1 H, exch D2O),

(65) PLATON: Spek, A. L.Acta Crystallogr., Sect. A1990, 46, C34.(66) Suffert, J.J. Org. Chem.1989, 54, 509-510.



2.616 (s, 1 H, exch D2O), 1.316 (s, 18 H), 1.304 (s, 9 H), 1.299 (s, 9H). 13C NMR (125 MHz, CDCl3; 293 K): aromatic region, expected,24 resonances, found, 24 resonances at 151.0, 150.9, 150.4, 148.2,148.0, 146.2, 145.4, 141.85, 141.80, 138.0, 130.3, 129.8, 129.3, 129.0,128.0, 127.6, 127.4, 127.2, 126.8, 125.24, 125.18, 125.13, 122.4, 122.0;aliphatic region, 86.0, 81.4, 81.1, 52.1, 34.52 (br), 34.49, 31.31, 31.29,31.28. IR (cm-1): 3557 (O-H), 3458 (O-H), 1567 (Ar), 1084 (C-O-C). A small amount of an unknown impurity was present:1H, 2.270(s); 13C, 125.5, 30.3.

Diol 6C. The product was changed from white to brown solid at308°C and melted and became a brown liquid at 320-322°C. FABMS(3-NBA) clusterm/z (% RA for m/z ) 200-1520): at (M- OCH3)+.1260.9 (25), 1261.9 (23), 1262.9 (68), 1263.9 (52), 1264.9 (98), 1265.9(67), 1266.9 (73), 1267.9 (43), 1268.9 (27), 1269.9 (13); at (M- OH)+,1274.9 (21), 1275.9 (18), 1276.9 (66), 1277.9 (50), 1278.9 (100), 1279.9(68), 1280.9 (76), 1281.9 (47), 1282.9 (31), 1283.9 (16).1H NMR (500MHz, EM ) -1.22, GB) 0.48, CDCl3, 1H-1H COSY cross-peaks inaromatic region; 293 K): 7.517 (t,J ) 1.5, 4 H, 7.468, 6.488), 7.468(t, J ) 1.5, 4 H, 7.517, 6.488), 7.359 (d,J ) 9, 4 H, 7.033), 7.260 (d,J ) 9, 4 H, 6.907), 7.033 (d,J ) 8, 4 H, 7.359), 6.907 (d,J ) 9, 4 H,7.260), 6.488 (t,J ) 1.5, 4 H, 7.517, 7.468), 2.800 (s, 2 H), 2.685 (s,6 H), 1.318 (s, 18 H), 1.310 (s, 18 H).13C NMR (125 MHz, CDCl3;293 K): aromatic region, expected, 14 resonances, found, 14 resonancesat 151.1, 150.5, 147.9, 145.7, 142.3, 138.0, 129.9, 128.9, 128.1, 127.50,127.42, 125.10, 125.02, 122.3; aliphatic region, 85.7, 81.4, 51.8, 34.55,34.42, 31.31 (EM) -2.88, GB) 0.48), 31.28. IR (cm-1): 3566 (O-H), 3453 (O-H), 1566 (Ar), 1082 (C-O-C). A small amount of anunknown impurity was present:1H, 2.270 (s);13C, 125.5, 30.3.

Diol 6D. The product was softened at 187°C and melted and becamea yellow liquid at 223-225 °C. FABMS (3-NBA) clusterm/z (% RAfor m/z ) 200-2700): at (M- OCH3)+, 1261.2 (35), 1262.2 (34),1263.2 (76), 1264.2 (57), 1265.2 (95), 1266.2 (70), 1267.2 (80), 1268.2(53), 1269.2 (36), 1270.2 (24); at (M- OH)+, 1275.2 (25), 1276.2(21), 1277.2 (68), 1278.2 (55), 1279.2 (100), 1280.2 (70), 1281.2 (82),1282.2 (50), 1283.2 (35), 1284.2 (18).1H NMR (500 MHz, EM )-1.20, GB) 0.80, CDCl3; 293 K): 7.497 (t,J ) 2, 2 H), 7.478 (t,J) 2, 2 H), 7.465 (t,J ) 2, 4 H), 7.332 (d,J ) 9, 2 H), 7.320 (d,J )9, 4 H), 7.200 (d,J ) 9, 2 H), 7.012 (d,J ) 8, 2 H), 6.974 (d,J ) 8,4 H), 6.925 (d,J ) 9, 2 H), 6.599 (t,J ) 1.5, 2 H), 6.551 (t,J ) 1.5,2 H), 2.865 (s, 3 H), 2.775 (s, 3 H), 2.736 (s, 2 H, D2O exch), 1.328(s, 9 H), 1.326 (s, 18 H), 1.297 (s, 9 H).13C{1H} DEPT (135°) NMR(125 MHz, CDCl3; 293 K): aromatic quaternary region, expected, 12resonances, found, 11 resonances at 151.0 (q), 150.6 (q), 148.0 (q),147.9 (q), 145.66 (q), 145.61 (q), 142.4 (q), 138.8 (q), 138.2 (q), 122.35(q), 122.32 (q); aromatic nonquaternary region, expected, 12 resonances,found 10 resonances at 130.2, 130.0, 129.4, 128.4, 127.8, 127.36,127.29, 125.1, 125.0, 124.8; aliphatic region, 86.14 (q), 86.11 (q), 81.3(q), 52.05, 52.03, 34.55 (q), 34.45 (q), 31.3. IR (cm-1): 3570 (O-H),3463 (O-H), 1567 (Ar), 1082 (C-O-C).

Diol 6E. The product was yellow solid at 160°C and melted andbecame a clear liquid at 197-200 °C. Anal. Calcd for C70H72O4Br4:C, 64.83; H, 5.60. Found: 65.30; H, 5.94. FABMS (3-NBA) clusterm/z (% RA for m/z ) 280-2400): at (M- OCH3)+, 1261.1 (23),1262.1 (20), 1263.1 (66), 1264.1 (52), 1265.1 (100), 1266.1 (66), 1267.1(76), 1268.1 (45), 1269.1 (38), 1270.1 (22); at (M- OH)+, 1275.1(19), 1276.1 (17), 1277.1 (54), 1278.1 (38), 1279.1 (80), 1280.1 (57),1281.1 (66), 1282.1 (41), 1283.1 (29), 1284.1 (15).1H NMR (500 MHz,CDCl3, 1H-1H fast COSY cross-peaks in aromatic region): 293 K,7.498 (bs, 4 H, 7.360, 6.730), 7.360 (bs, 4 H, 7.498, 6.730), 7.327 (d,J ) 8, 4 H, 6.960), 7.286 (d,J ) 8, 4 H, 7.052), 7.052 (d,J ) 8, 4 H,7.286), 6.960 (d,J ) 8, 4 H, 7.327), 6.730 (bs, 4 H, 7.498, 7.360),2.953 (s, 6 H), 2.669 (s, 2 H, D2O exch), 1.341 (s, 18 H), 1.324 (s, 18H). 13C{1H} DEPT (135°) NMR (125 MHz, CDCl3; 293 K): aromaticquaternary region, expected, 7 resonances, found, 7 resonances at 150.9(q), 150.3 (q), 148.1 (q), 145.0 (q), 142.1 (q), 138.7 (q), 122.1 (q);aromatic nonquaternary region, expected, 7 resonances, found 6

resonances at 130.4, 129.7, 127.9, 127.3, 127.2, 125.1; aliphatic region,86.1 (q), 81.2 (q), 52.1, 34.5 (q), 31.3.1H NMR (500 MHz, C6D6,1H-1H fast COSY cross-peaks in aromatic region; 293 K): 7.850 (bs,4 H, 7.451, 7.150), 7.451 (bs, 4 H, 7.850, 7.150), 7.328 (d,J ) 8, 4 H,7.282), 7.282 (d,J ) 8, 4 H, 7.328), 7.174 (d,J ) 8, 4 H, 7.039),7.150 (bs, 4 H, 7.850, 7.451), 7.039 (d,J ) 8, 4 H, 7.174), 2.821 (s,6 H), 2.150 (bs, 2 H), 1.341 (s, 18 H), 1.324 (s, 18 H).13C{1H} DEPT(135°) NMR (125 MHz, C6D6; 293 K): aromatic quaternary region,expected, 7 resonances, found, 6 resonances at 150.9 (q), 149.5 (q),146.7 (q), 143.3 (q), 139.9 (q), 122.9 (q); aromatic nonquaternary region,expected, 7 resonances, found 7 resonances at 131.1, 130.9, 128.67,128.3, 128.0, 126.1, 125.7; aliphatic region, 86.9 (q), 81.6 (q), 52.3,34.9 (q), 34.8(q), 31.72, 31.66. An additional resonance at 128.64 ppmwas assigned to C6D5H. IR (cm-1): 3433 (O-H), 1567 (Ar), 1080(C-O-C).

Tetrabromocalix[4]arene Tetraethers 7. A 100 mL flask withsidearm was charged with NaH (0.300 g of 60% dispersion in mineraloil, 7.722 mmol). After removal of mineral oil with pentane undernitrogen flow, THF (15 mL) was added. The reaction mixture wascooled with an ice bath, and then diol6A (1.669 g, 1.287 mmol) inTHF (30 mL) was added. The resultant, stirred suspension was allowedto attain ambient temperature over a priod of∼2 h. Subsequently,iodomethane (1.30 mL, 20.6 mmol) was added at 0°C. The reactionmixture was allowed to attain ambient temperature overnight. Afterthe usual aqueous workup (ether, MgSO4), the white or light yellowsolid was crystallized from ether/MeOH to give pure product7A asindicated below. An analogous procedure was used to obtain7C-E.The calculated isotopic intensities at (M- OCH3)+ in FABMS of7A-E are as follows: C71H73O3Br4, 1289.2 (14), 1290.2 (11), 1291.2(61), 1292.2 (46), 1293.2 (100), 1294.2 (70), 1295.2 (80), 1296.2 (49),1297.2 (31), 1298.2 (15).

Tetraether 7A. From diol 6A (1.669 g), 1.042 g (62%) of7A aswhite powder was obtained. The product was softened at 305°C andmelted and became a brown liquid at 324-326 °C. Anal. Calcd forC72H76O4Br4: C, 65.27; H, 5.78. Found: 64.98; H, 5.89. FABMS(3-NBA) clusterm/z (% RA for m/z ) 200-1460): at (M- OCH3)+,1289.2 (25), 1290.2 (20), 1291.2 (70), 1292.2 (52), 1293.2 (100), 1294.2(69), 1295.2 (73), 1296.2 (46), 1297.2 (30), 1298.2 (15).1H NMR (500MHz, CDCl3, EM ) -0.68, GB) 0.46, CDCl3, 1H-1H COSY cross-peaks in aromatic region; 293 K): 7.504, 7.500 (d,J ) 1.5, d,J )1.5, 8 H, 6.848, 6.434), 7.278 (d,J ) 9, 8 H, 7.034), 7.034 (d,J ) 9,8 H, 7.278), 6.848 (bs, 2 H, 7.504, 7.500), 6.834 (bs, 2 H, 7.504, 7.500),2.861 (s, 12 H), 1.312 (s, 36 H). (COSY cross-peaks are not resolvedfor the J ) 1.5 multiplets.)13C NMR (125 MHz, CDCl3; 293 K):aromatic region, expected, 12 resonances, found, 12 resonances at 150.4,146.3, 145.7, 137.8, 130.1, 129.3, 128.9, 128.4, 126.4, 124.8, 121.9,121.8; aliphatic region, 86.1, 52.2, 34.5, 31.3. IR (cm-1): 1563 (Ar),1086 (C-O-C).

Tetraether 7C. From 3.5:1 mixture of diols6B,C (0.102 g, 0.079mmol), 0.110 g of yellow viscous solid was obtained. PTLC (10%benzene in hexane) of 0.032 g of the crude mixture gave 0.0268 g(88%) of 7D,C (3.6:1) as a clear viscous solid.

From 1:8 mixture of diols6B,C (20.0 mg, 0.016 mmol), 15.7 mg(74%, single spot in TLC, 3% ether in hexane) of7D,C (1:8) as yellowviscous solid was obtained. Treatment with ether/MeOH did notimprove the purity of the product.

1H NMR (500 MHz, CDCl3, EM ) -1.30, GB ) 0.46, 1H-1HCOSY cross-peaks in aromatic region; 293 K): 7.466 (d,J ) 1.5, 8H, 7.010), 7.322 (d,J ) 9, 8 H, 7.131), 7.131 (d,J ) 9, 8 H, 7.322),7.010 (t,J ) 1.5, 4 H, 7.466), 2.883 (s, 12 H), 1.323 (s, 36 H).13CNMR (125 MHz, CDCl3; 293 K): aromatic region, expected, 8resonances, found, 8 resonances at 150.63, 146.04, 137.9, 129.73,128.96, 127.2, 124.94, 121.74; aliphatic region, 86.10, 52.15, 34.53,31.32. IR (cm-1): 1566 (Ar), 1083 (C-O-C).

Tetraether 7D. From diol6D (0.348 g, 0.268 mmol), 0.299 g (84%)of 7D as white powder was obtained. The product was softened at 152



°C, melted at 168-170°C, and became a clear liquid at 178°C. Fromother reactions, 0.573 g (63%) and 0.773 g (83%) of7D as whitepowder after treatment with ether/MeOH were obtained from 0.909 g(0.698 mmol) and 0.914 g (0.705 mmol) of diol6D, respectively. Theproduct was softened at 189°C and melted and became clear liquid at197-200°C. Anal. Calcd for C70H72O4Br4: C, 65.27; H, 5.78. Found:65.16; H, 5.25. FABMS (3-NBA) clusterm/z (% RA for m/z ) 200-2600): at (M- OCH3)+, 1289.2 (22), 1290.2 (18), 1291.2 (67), 1292.2(52), 1293.3 (100), 1294.2 (71), 1295.2 (77), 1296.2 (50), 1297.2 (29),1298.3 (15).1H NMR (500 MHz, EM ) -1.20, GB) 0.85, CDCl3,1H-1H FastCOSY cross-peaks in aromatic region; 293 K): 7.522 (t,J) 2, 2H, 7.409, 7.037), 7.502 (t,J ) 2, 2 H, 7.409, 6.965), 7.409 (t,J ) 2, 2H, 7.522, 7.037), 7.409 (t,J ) 2, 2H, 7.502, 6.965), 7.312 (d,J ) 9, 4 H, 7.145), 7.312 (d,J ) 9, 2 H, 7.010), 7.268 (d,J ) 9, 2 H,7.060), 7.145 (d,J ) 8, 4 H, 7.312), 7.060 (d,J ) 8, 2 H, 7.268),7.037 (t,J ) 2, 2H, 7.522, 7.409), 7.010 (d,J ) 9, 2 H, 7.312), 6.965(t, J ) 2, 2H, 7.502, 7.409), 2.935 (s, 3 H), 2.919 (s, 6 H), 2.895 (s,3 H), 1.334 (s, 9 H), 1.329 (s, 18 H), 1.314 (s, 9 H).13C{1H} DEPT(135°) NMR (125 MHz, CDCl3): 293 K, aromatic quaternary region,expected, 12 resonances, found, 12 resonances at 150.53 (q), 150.49(q), 150.40 (q), 146.3 (q), 146.1 (q), 145.9 (q), 145.8 (q), 138.23 (q),138.17 (q), 137.7 (q), 121.84 (q), 121.67 (q); aromatic nonquaternaryregion, expected, 12 resonances, found 12 resonances at 130.3, 129.84,129.80, 129.5, 128.88, 128.76, 128.35, 127.6, 127.4, 125.04, 124.93(overlapped with7C in mixtures), 124.8; aliphatic region, 86.09 (q),86.04 (q), 52.4, 52.21, 52.12, 34.53 (q) (overlapped with7C inmixtures), 34.51 (q), 31.35. IR (cm-1): 1564 (Ar), 1081 (C-O-C).

Tetraether 7E. From diol6E (0.291 g, 0.225 mmol), 0.112 g (38%)of 7E as white crystals was obtained. Mp: 295-298°C. Other reactionsfrom diol 6E (0.345 g, 0.266 mmol; 0.102 g, 0.079 mmol) gave 0.254g (61%) and 0.058 g (57%), respectively, of7E as white solids. Theproduct was softened at 304°C and melted and became brown liquidat 312-314 °C. Anal. Calcd for C72H76O4Br4: C, 65.27; H, 5.78.Found: C, 65.29; H, 5.26. FABMS (3-NBA) clusterm/z (% RA form/z ) 240-2500): at (M- OCH3)+, 1289.2 (20), 1290.2 (17), 1291.2(65), 1292.2 (50), 1293.2 (100), 1294.2 (70), 1295.2 (78), 1296.2 (46),1297.2 (31), 1298.2 (14).1H NMR (300 MHz, EM ) -1.30, GB)0.85, CDCl3; 293 K): 7.456 (d,J ) 2, 8 H), 7.322 (AB,J ) 9, 8 H),7.147 (t,J ) 2, 4 H), 7.119 (AB,J ) 9, 8 H), 2.932 (s, 12 H), 1.338(s, 36 H).1H NMR (500 MHz, C6D6, 1H-1H COSY cross-peaks inaromatic region; 293 K): 7.699 (d,J ) 1.5, 8 H, 7.553), 7.553 (bs, 4H, 7.699), 7.301 (d,J ) 9, 8 H, 7.226), 7.226 (d,J ) 9, 8 H, 7.301),2.783 (s, 12 H), 1.149 (s, 36 H).13C{1H} DEPT (135°) NMR (125MHz, C6D6; 293 K): aromatic quaternary region, expected, 4 reso-nances, found, 4 resonances at 150.8 (q), 146.7 (q), 140.2 (q), 122.5(q); aromatic nonquaternary region, expected, 4 resonances, found 4resonances at 131.6, 129.3, 128.4, 126.2; aliphatic region, 86.9 (q),52.3, 34.8 (q), 31.7. IR (cm-1): 1565 (Ar), 1083 (C-O-C).

24-Ether 1-(OMe)24. t-BuLi (0.136 mL of 1.855 M solution inpentane,66 0.253 mmol) was added to bromopentaether8 (0.186 g,0.117 mmol) in THF (1.3 mL) in a heavy-wall Schlenk vessel at-78°C. After 2 h at -78 °C, the reaction mixture was allowed to attain-20°C for 10 min and then recooled to-78°C. Following the additionof ZnCl2 (0.13 mL of 1.03 M solution in ether, 0.134 mmol), thereaction mixture was allowed to attain ambient temperature. In aVacuum Atmospheres glovebox, Pd(PPh3)4 (5.0 mg, 4.3µmol) andtetrabromocalix[4]arene tetraether7E (25.9 mg, 19.5µmol) were addedto the reaction mixture. Subsequently, the reaction mixture was stirredat 100 °C for 3 days. Following the usual aqueous workup, twoconsecutive purifications by column chromatography (4-8% ether inhexane) and treatments with MeOH/ether gave 24-ether1-(OMe)24 asa white powder (54.7 mg, 40%). Three additional reactions, each startingfrom 0.2-0.400 g of bromopentaether8, gave 24-ether in 28, 13, and16% yields.

The following side products were isolated by column chromatog-raphy and treated with ether/MeOH to give white powders: dendrimer

quenching product8-H (40.7 mg, 23%); homocoupling product10 (24.7mg, 7%); tricoupling product12 (1.8 mg, 1%). Another isolation of10, without treatment with ether/MeOH, gave 16.4 mg (9%) of clearoil.

24-Ether 1-(OMe)24: softening at 186°C and melting at 200-201°C (clear liquid). Anal. Calcd for C504H592O24: C, 86.06; H, 8.48.Found: 86.60; H, 8.22. FABMS (3-NBA) clusterm/z (% RA for m/z) 3200-7400): at (M- OCH3)+, 6998.5 (35), 6999.5 (52), 7000.5(74), 7001.5 (90), 7002.5 (100), 7003.5 (75), 7004.5 (71), 7005.5 (49),7006.5 (31); calcd for C503H589O23 at (M - OCH3)+, 6998.5 (11), 6999.5(32), 7000.5 (61), 7001.5 (88), 7002.5 (100), 7003.5 (96), 7004.5 (78),7005.5 (56), 7006.5 (35).1H NMR (500 MHz) spectra for1-(OMe)24

were obtained in C6D6 (293-348 K), toluene-d8 (293-383 K), andtetrachloroethylene (293-383 K). The best resolved spectra wereobtained in benzene-d6, and only those are listed below.1H NMR (500MHz, C6D6): 293 K, 8.10-7.00 (br m, 196 H), 3.264 (s, 12 H), 2.947(s, 48 H), 2.869 (s, 12 H), 1.211 (s, 144 H), 1.205 (s, 144 H), 1.062 (s,36 H); 328 K, 8.10-7.00 (br m, 196 H), 3.265 (s, 12 H), 2.949 (s, 48H), 2.885 (s, 12 H), 1.214 (s, 288 H), 1.086 (s, 36 H).1H NMR (500MHz, EM ) -1.20, GB) 0.90, benzene-d6, 1H-1H COSY cross-peaks in aromatic region; 348 K): 7.97 (br, 4 H), 7.90 (br, 8 H), 7.817(d, J ) 2, 16 H, 7.673), 7.673 (t,J ) 2, 8 H, 7.817), 7.636 (d,J ) 9,8 H, 7.260), 7.455 (d,J ) 9, 32 H, 7.227), 7.448 (d,J ) 8, 32 H,7.219), 7.423 (d,J ) 8, 8 H, 7.352), 7.352 (d,J ) 8, 8 H, 7.423),7.260 (d,J ) 9, 8 H, 7.636), 7.227 (d,J ) 9, 32 H, 7.455), 7.219 (d,J ) 9, 32 H, 7.448), 3.262 (s, 12 H), 2.952 (s, 48 H), 2.896 (s, 12 H),1.220 (s, 288 H), 1.106 (s, 36 H).13C{1H} DEPT (135°) NMR (125MHz, EM ) -0.90 Hz, GB) 1.90 Hz, C6D6, 1H-13C HMQC-GScross-peaks in aromatic nonquaternary region; 348 K): aromaticquaternary region, expected, 10 resonances, found, 9 resonances at 150.3(q), 150.0 (q), 145.02 (q), 144.98 (q), 143.8 (q), 143.2 (q), 142.8 (q),140.6 (q), 140.5 (q); aromatic nonquaternary region, expected, 10resonances, found 9 resonances at 131.2 (7.352), 130.0 (7.673), 129.6(7.455, 7.448), 128.8 (7.636), 127.9 (7.817), 127.5 (br, 7.90), 127.0(7.423), 125.7 (7.260), 125.1 (7.227, 7.219); aliphatic region, 88.5 (q),88.1 (q), 87.9 (q), 52.90, 52.87, 52.6, 34.9 (q), 31.99, 31.96 (EM)-0.9, GB) 1.0). Note: the13C resonance at 125.1 ppm correspondsto two resonances at 125.15 and 125.13 (EM) -0.77 and GB) 0.40)at 293 K. IR (cm-1): 1595 (ArH), 1082 (C-O-C). GPC/MALS: Table4s, Supporting Information.

Octaether 2-(OMe)8. A procedure analogous to that for1-(OMe)24

was used.t-BuLi (0.189 mL of 1.855 M solution in pentane,66 0.351mmol) was added to bromoether9 (76.7 mg, 0.165 mmol) in THF(1.5 mL) in a heavy-wall Schlenk vessel at-78 °C. After 2 h at-78°C, the reaction mixture was warmed to-20 °C for 10 min and thenrecooled to-78 °C. Following addition of ZnCl2 (0.17 mL of 1.03 Msolution in ether, 0.175 mmol), the reaction mixture was allowed toattain ambient temperature. In a Vacuum Atmospheres glovebox,Pd(PPh3)4 (6.0 mg, 5.2µmol) and tetrabromocalix[4]arene tetraether7E (36.5 mg, 27.5µmol) were added to the reaction mixture.Subsequently, the reaction mixture was heated at 100°C for 3 days.Following the usual workup, column chromatography (preheated silicaat 200°C overnight, 3-5% ether in hexane) and treatment with ether/MeOH, 8.7 mg (12%) of2-(OMe)8 as a white powder was obtained.(The purity of fractions corresponding to2-(OMe)8 was checked with1H NMR before combining and filtering through the cotton plug.)Similarly, 6.6 mg (10%) of homocoupling side product11was obtainedas a white powder.

A second reaction yielded 23.6 mg (16%) of2-(OMe)8 as a whitepowder; it was performed on a double scale usingt-BuLi (0.45 mL of1.5 M solution in pentane, 0.675 mmol), bromoether9 (150 mg, 0.322mmol) in THF (3.0 mL), and tetraether7E (75.0 mg, 56.7µmol).

A third reaction yielded 21.7 mg (16%) of2-(OMe)8 as a whitepowder; it was carried out usingt-BuLi (0.45 mL of 1.5 M solution inpentane, 0.675 mmol), bromoether9 (150 mg, 0.322 mmol) in THF(3.0 mL), and tetraether7E (70.1 mg, 52.9µmol).



Octaether 2-(OMe)8: softening at 201°C and melting at 226-229°C. Anal. Calcd for C184H208O8: C, 86.75; H, 8.23. Found: 85.39; H,7.99. FABMS (3-NBA) clusterm/z (% RA for m/z ) 700-4300): at(M - OCH3)+, 2514.6 (65), 2515.6 (100), 2516.6 (95), 2517.6 (65),2518.5 (40); calcd for C183H205O7, 2514.6 (45), 2515.6 (95), 2516.6(100), 2517.6 (70), 2518.6 (35).1H NMR (500 MHz, C6D6, 1H-1HCOSY cross-peaks in aromatic region; 293 K): 8.06 (br, 4 H, 7.95),7.95 (br, 8 H, 8.06), 7.627 (d,J ) 8, 8 H, 7.218), 7.533 (d,J ) 8, 16H, 7.265), 7.472 (d,J ) 8, 8 H, 7.439), 7.439 (d,J ) 8, 8 H, 7.472),7.265 (d,J ) 8, 16 H, 7.533), 7.218 (d,J ) 8, 8 H, 7.627), 3.132 (s,12 H), 3.035 (s, 12 H), 1.211 (s, 72 H), 1.060 (s, 36 H).13C{1H} DEPT(135°) NMR (125 MHz, C6D6, 1H-13C HSQC-GS cross-peaks inaromatic nonquaternary region; 293 K): aromatic quaternary region,expected, 8 resonances, found, 7 resonances at 150.1 (q), 150.0 (q),145.3 (q), 144.3 (q), 142.3 (q), 140.54 (q), 140.47 (q); aromaticnonquaternary region, expected, 8 resonances, found 8 resonances at130.4 (8.06, br), 130.1 (7.472), 129.5 (7.533), 128.8 (7.627), 127.5(7.95), 127.3 (7.439), 125.8 (7.218), 125.3 (7.265); aliphatic region,88.0 (q), 52.6, 52.4, 34.78 (q), 34.72 (q), 31.8. IR (cm-1): 1595 (ArH),1081 (C-O-C). GPC/MALS: Table 4s, Supporting Information.

Carbopolyanion 124- for NMR or SANS Studies. Polyether1-(OMe)24 (11.40 mg, 1.62µmol) was placed in a glass reaction vessel,equipped with a 5-mm NMR sample tube or a quartz cylindrical cell(Figure 13). Carbopolyanion was generated by following the procedurefor polyradical1, which is described in the following paragraph. Afterthe solution of carbopolyanion was filtered into the NMR tube or SANScell, the sample vessel was flame sealed and stored in liquid nitrogenfor subsequent studies.1H NMR (500 MHz, THF-d8): 293 K, 7.40-6.10 (m, 196 H), 1.164 (s, 320 H); 193 K, 7.8-5.3 (bm), 1.4-0.9 (bm),

both resonances for THF-d7 remain relatively sharp.13C NMR (125MHz, pulse delay) 0.1 s, acquisition time) 0.5 s, 7× 104 scans,THF-d8; 293 K): aromatic region, expected, 24 resonances, found, 10resonances at 152.4, 149.2, 145.6, 144.3, 132.3, 125.6, 120.9, 120.3,119.3, 118.2; aliphatic region, 85.8 (Ar3C), 34.2, 32.6, 32.4 (30.7, imp).

Polyradicals 1 and 2. Samples for Magnetic Measurements.24-Ether1-(OMe)24 (0.50-1.60 mg, 70-230 nmol) was placed in a glassreaction vessel, equipped with coarse glass frit, two high-vacuum PTFEstopcocks, and a 5-mm o.d. quartz tube with thin bottom 6 cm fromthe end of the tube (Figure 13). The vessel containing polyether washeated overnight under vacuum; i.e., part of the vessel containingpolyether was immersed in an oil bath at 60°C and the rest of thevessel was heated at 200°C using heating tape. Subsequently, the vesselwas transferred to a glovebox and a small drop of Na/K alloy wasadded. Following attachment of the vessel to vacuum line, Na/K wasallowed to come in contact with polyether, and THF-d8 (0.06-0.08mL, 99.95% D) was immediately vacuum-transferred from sodium/benzophenone. After 3-5 days of stirring at 10°C, the reaction mixturewas filtered under temperature gradient into the quartz tube. (Analternative procedure was based upon preparation of carbopolyanionin a glovebox equipped with oven/antechamber.) Iodine (99.999%,ultradry) was vacuum-transferred in small portions to the reactionmixture at-103 to-106 °C, until the final yellow-brown color of1appeared. The tube was flame sealed (total length of about 20 cm) andstored in liquid nitrogen prior to insertion to SQUID magnetometer.Analogous procedures were used for octaradical2 and tetraradical3.The dilute sample of2 was prepared using a previously reported method,in which the measured amount of polyradical is not known.21

Samples for SANS Measurements.The procedure was based upon10-30 mg of 24-ether1-(OMe)24; quartz cylindrical cells with 2-mmand 5-mm optical paths were used (Figure 13).

Approximately twice the volume of THF-d8, compared to the samplesfor magnetic measurements, was used for generation of carbopolyanion.For polyradical generation, iodine and THF-d8 were vacuum transferredin small portions until the desired color and volume in the cell wereattained. Subsequently, the cells were flame sealed; the quartz seal,above the cylindrical part of the cell, had to be<2 cm long to providean adequate fit to the SANS sample holder.

Quenching Studies. 1-H24. A cylindrical SANS cell, containing124-

(prepared from 29.56 mg, 4.20µmol, of 1-(OMe)24) in THF-d8, wasimmersed under argon-bubbled MeOH (100 mL) at room temperature.The cell was cracked, and the brown mixture was leaking out to be incontact with MeOH to form a white precipitate. Following the usualaqueous workup with hexane, PTLC (25% chloroform in hexane), andtreatment with ether/MeOH, 10.9 mg (41%) of the less polar (F1) and2.6 mg (10%) of the more polar (F2) fractions of1-H24 were obtainedas white powders. Although theRf values for F1 and F2 are significantlydifferent on silica, their1H NMR spectra are almost identical.

F1: softening at 194°C and melting at 204-206 °C (clear liquid).1H NMR (500 MHz, CDCl3; 293 K): 7.25-6.65 (m, 196 H), 5.45-5.35 (m, 4 H), 5.219, 5.178 (s, s, 19 H), 1.35-1.05 (m, 325 H).13CNMR (125 MHz, CDCl3; 293 K): aromatic region, expected 20resonances, found 18 resonances at 148.5, 144.5 (br), 143.7 (br), 142.5,141.34, 141.26, 140.5 (br), 138.4, 129.5, 128.86, 128.83, 128.6, 128.4,126.6, 126.2 (br), 125.5, 125.3-124.8 (br), 124.9; aliphatic region, 56.7(br), 56.4 (br), 55.9, 34.3, 31.1. IR (cm-1): 1595 (ArH). GPC/MALS:Table 4s, Supporting Information. SANS (THF-d8): see main text.

F2: softening at 190°C and melting at 204-206°C (yellow liquid).1H NMR (500 MHz, CDCl3; 293 K): 7.23-6.60 (m, 196 H), 5.45-5.35 (m, 4 H), 5.217, 5.178 (s, s, 18 H), 1.37-1.00 (m, 317 H). IR(cm-1): 1595 (ArH).

2-H8. A small portion of polyradical2 in THF (prepared from 9.4mg of octaether1-(OMe)8) was transferred to a quartz tube for magneticmeasurements, and the remaining polyradical was stirred with Na/K at-95 to-78 °C for several hours and then quenched with MeOH. Theusual aqueous workup, followed by PTLC (2.5% ether in hexane), gave

Figure 13. Vessel for preparation of polyanions and polyradicals forSQUID magnetometry (tube A), ESR spectroscopy (tube B), SANS(cylindrical cell C), and NMR spectroscopy (sample tube not shown): (a)sample compartment with Teflon-coated magnetic stirbar; (b) glass frit(course); (c) Pyrex-to-quartz seal; (d) thin bottom (∼6 cm from the end ofthe tube). Solv-seal joints and Kontes (or Chemglass) vacuum stopcocksare used.



2-H8 as glassy solid (6.1 mg, 70%) with softening at 190°C and meltingat 202-205 °C (yellow liquid). FABMS (3-NBA) clusterm/z (% RAfor m/z ) 2288-2333, S/N≈ 2.5/1): 2305.5 (65), 2306.5 (85), 2307.5(95), 2308.5 (100), 2309.5 (85), 2310.5 (65); calcd for C176H193 (M +H)+, 2306.5 (50), 2307.5 (100), 2308.5 (98), 2309.5 (65), 2310.5 (30).1H NMR (500 MHz, CDCl3; 293 K): 7.5-6.7 (m, 60 H), 5.8-4.4 (8H), 1.35-1.1 (m, 107 H). IR (cm-1): 1594 (ArH).

SQUID Magnetometry. A Quantum Design (San Diego, CA)MPMS5S (with continuous temperature control) was used. The sampletubes were inserted to the magnetometer at low temperature underhelium atmosphere and then evacuated and purged with helium, asdescribed elsewhere. Following the measurements, sample tubes werestored at ambient temperature for several weeks, until they werediamagnetic in the 1.8-150 K range. Such samples were carefullyreinserted to the magnetometer, with the sample chamber at 200 or290 K. Then the temperature was slowly lowered to 10 K to condensethe solvent and to freeze the sample. The identical sequence ofmeasurements, as for the original sample, was carried out. The resultantdata were used for the point-by-point correction for diamagnetism.

Numerical Curve Fitting for Magnetic Data. The SigmaPlot forWindows software package was used for numerical curve fitting. Thereliability of a fit is measured by the parameter dependence, which isdefined as follows:dependence) 1 - ((Variance of the parameter,other parameters constant)/(Variance of the parameter, other param-eters changing)). Values close to 1 indicate overparametrized fit.

Up to four variable parameters,J/k (spin coupling constant inKelvins),N (number of moles of polyradical),Θ (mean field parameterfor small intermolecular magnetic interactions), andMdia (correctionfor diamagnetism), are used for fittingMT vs T data over wide rangeof T. In 1, Θ does not affect the fits and it is omitted (Θ ) 0), as theintermolecular magnetic interactions are essentially negligible. Withthe exception of one sample of1, in which Mdia was more than 1% ofthe total diamagnetism after point-by-point correction,Mdia ) 0 wasset. Thus, no more than three variable parameters were used. Equationsfor magnetization,M(T,H), are obtained using the standard statisticalmechanical procedures for energy eigenvalues, derived from HeisenbergHamiltonian.26,46-48

M vsH data at low temperatures (T ) 1.8, 3, 5, 10 K) were analyzedwith Brillouin functions as described in the text.

For 1, an alternative procedure for analysis of theM vs H datainvolved fitting of theM vsH/T data to linear combinations of Brillouinfunctions (Β(Si)) weighed with fractions (xi) of spin systems with spinSi. Two different percolation models were used to obtain values ofxi

andSi.The first percolation model, which was employed in the preliminary

communication,22 used eq 3.

The model assumed ferromagnetic coupling between all nearestneighbor arylmethyls. Two variable parameters,p andMsat, were used.Parameterp was the probability that triarylmethyl site had an intactradical. Because the value ofMsatwas a variable parameter, this modelwas not quantitative. Enumeration of configurations with 0-4 defects

at the four 4-biphenyl-substituted sites gave the following values ofxi

and Si: xi ) p4, 4p3(1 - p), 6p2(1 - p)2, 4p(1 - p)3, (1 - p)4, and8[p3(1 - p) + 3p2(1 - p)2 + 3p(1 - p)3 + (1 - p)4] and Si ) 2 +10p, 1.5 + 8p, 1 + 6p, 0.5 + 4p, 2p, and p, where i ) 1, 2, ... 6.Because in eq 2 the Brillouin functions were not explicitly multipliedby values of spin,Si, fractionsxi includedSi. Therefore, spin-averagespin Ss should be defined as shown in eq 4.51

For polyradical1, eq 4 could be simplified:Ss ) 12p/(9 - 8p).The second percolation model, used in this work, was based on

eq 5:

CoefficientsAi and spin valuesSi are optimized through two variableparameters,q andp. Parameterp was defined as in the first percolationmodel. Parameterq was the probability that a biphenylene moietymediates ferromagnetic (vs antiferromagnetic) coupling. This modelwas quantitative, using number of moles (N) of polyradical (orpolyether) as an input;Msatwas not a variable parameter. Configurationswith 0-4 defects at the four 4-biphenyl-substituted sites and 0-4antiferromagnetic couplings across four biphenylene coupling units wereenumerated, leading to 1280 spin systems; however, only 10 spin values(Si, i ) 0-9) were unique. Elucidation of all values ofSi and coefficientsAi for 24-radical1 followed general methods as reported elsewhere.28a

Acknowledgment. This research was supported by theNational Science Foundation (Chemistry Division) and theNational Center for Neutron Research (beam time on NG3,Grant Nos. 1781 and 2471). We thank Drs. Richard Schoemakerand Ronald Cerny for their help with NMR spectral determina-tions and mass spectral analyses. We thank Drs. Maren Pinkand Victor G. Young, Jr., of the X-ray CrystallographicLaboratory at the University of Minnesota for the structuredetermination of compound7E. S.R. thanks the EuropeanMolecular Biology Laboratory (Hamburg, Germany) for theATSAS program package for numerical fitting of SANS data.

Supporting Information Available: An experimental section(materials and special procedures, NMR spectroscopy and otheranalyses, characterization data for8-H, 8-D, 10, 11, and12-(OMe)19, SANS instrumental setup and sample handling,numerical curve fitting for the SANS data), Tables 1s-4s(summary of NMR data for6 and7, summary of GPC/MALSdata), Figures 1s-6s (FAB MS for2-(OMe)8 and12-(OMe)19,summary plot of GPC/MALS data, selected NMR spectra for2-(OMe)8, SANS plots for polyradical1 and polyanion124-),and an X-ray crystallographic file for7E in CIF format. Thismaterial is available free of charge via the Internet athttp://pubs.acs.org.

JA031548J

M/Msat) ΣiΒ(Si)xi/Σixi (3)

Ss ) ΣiSixi/Σixi (4)

M ) 11180NΣiAiB(Si) (5)



polyradical with very high spin of s ) 10 and its derivatives: s

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